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    <title>Pinboard (cshalizi)</title>
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    <description>recent bookmarks from cshalizi</description>
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  </channel><item rdf:about="https://arxiv.org/abs/2503.15200">
    <title>[2503.15200] Partially Observable Reinforcement Learning with Memory Traces</title>
    <dc:date>2025-09-05T16:19:08+00:00</dc:date>
    <link>https://arxiv.org/abs/2503.15200</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Partially observable environments present a considerable computational challenge in reinforcement learning due to the need to consider long histories. Learning with a finite window of observations quickly becomes intractable as the window length grows. In this work, we introduce memory traces. Inspired by eligibility traces, these are compact representations of the history of observations in the form of exponential moving averages. We prove sample complexity bounds for the problem of offline on-policy evaluation that quantify the return errors achieved with memory traces for the class of Lipschitz continuous value estimates. We establish a close connection to the window approach, and demonstrate that, in certain environments, learning with memory traces is significantly more sample efficient. Finally, we underline the effectiveness of memory traces empirically in online reinforcement learning experiments for both value prediction and control."]]></description>
<dc:subject>reinforcement_learning control_theory_and_control_engineering re:AoS_project in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:909b6539c26c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:reinforcement_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
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</item>
<item rdf:about="https://doi.org/10.1016/0022-2496(66)90020-4">
    <title>The structure of responses to a sequence of binary events - ScienceDirect</title>
    <dc:date>2023-04-24T21:43:30+00:00</dc:date>
    <link>https://doi.org/10.1016/0022-2496(66)90020-4</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A procedure developed by Foulkes for determining the structure of a sequence of binary events was found to be a useful base-line model of structure determination by human subjects. The structure is represented in terms of the subsequences of events (states) which lead to different probabilities of the events. While the subjects' behavior after each state is not given by the Foulkes procedure, their behavior appeared to be largely a function of the probabilities of the events after each state (matching) and the lastest event in the state (positive recency)."

--- The Foulkes (1959) paper lying behind this is truly wild as a flash of genius but doesn't seem to be online anywhere.  (I may rectify this.)]]></description>
<dc:subject>have_read markov_models cognitive_science variable-length_markov_models_aka_context_trees statistical_inference_for_stochastic_processes re:AoS_project cleaning_out_the_filing_cabinet_for_the_first_time_since_2005 re:dissertation prediction in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:851a2a33fb27/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cognitive_science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variable-length_markov_models_aka_context_trees"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cleaning_out_the_filing_cabinet_for_the_first_time_since_2005"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:dissertation"/>
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<item rdf:about="https://link.springer.com/chapter/10.1007/bfb0008474">
    <title>Stochastic realization problems | SpringerLink</title>
    <dc:date>2023-03-27T15:07:23+00:00</dc:date>
    <link>https://link.springer.com/chapter/10.1007/bfb0008474</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The stochastic realization problem asks for the existence and the classification of all stochastic systems for which the output process equals a given process in distribution or almost surely. This is a fundamental problem of system and control theory. The stochastic realization problem is of importance to modelling by stochastic systems in engineering, biology, economics etc. Several stochastic systems are mentioned for which the solution of the stochastic realization problem may be useful. As an example recent research on the stochastic realization problem for the Gaussian factor model and a Gaussian factor system is discussed."]]></description>
<dc:subject>to:NB stochastic_processes re:AoS_project re:almost_none via:mraginsky</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f2eb81ce173e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
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<item rdf:about="https://onlinelibrary.wiley.com/doi/abs/10.1111/jtsa.12615">
    <title>Variable Length Markov Chain with Exogenous Covariates - Zambom - - Journal of Time Series Analysis - Wiley Online Library</title>
    <dc:date>2021-08-16T03:26:10+00:00</dc:date>
    <link>https://onlinelibrary.wiley.com/doi/abs/10.1111/jtsa.12615</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Markov Chains with variable length are useful stochastic models for data compression that avoid the curse of dimensionality faced by full Markov Chains. In this paper we introduce a Variable Length Markov Chain whose transition probabilities depend not only on the state history but also on exogenous covariates through a generalized linear model. The goal of the proposed procedure is to estimate not only the context of the process, that is, the history of the process that is relevant for predicting the next state, but also the coefficients corresponding to the significant exogenous variables. The proposed method is consistent in the sense that the probability that the estimated context and the coefficients are equal to the true data generating mechanism tends to 1 as the sample size increases. Simulations suggest that, when covariates do contribute to the transition probabilities, the proposed procedure can recover both the tree structure and the regression parameters. It outperforms variable length Markov Chains when covariates are present while yielding comparable results when covariates are absent. For models with fixed length, the accuracy of the proposed algorithm in recovering the true data generating mechanism is close to the methods available in the literature. The proposed methodology is used to predict the gains and losses of the Hang Seng Index based on its own history and three large stock market indices."]]></description>
<dc:subject>to:NB time_series markov_models re:AoS_project statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:dd1ba3024572/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
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</item>
<item rdf:about="https://arxiv.org/abs/1406.5362">
    <title>[1406.5362] Predicting the Future Behavior of a Time-Varying Probability Distribution</title>
    <dc:date>2021-04-21T19:54:13+00:00</dc:date>
    <link>https://arxiv.org/abs/1406.5362</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study the problem of predicting the future, though only in the probabilistic sense of estimating a future state of a time-varying probability distribution. This is not only an interesting academic problem, but solving this extrapolation problem also has many practical application, e.g. for training classifiers that have to operate under time-varying conditions. Our main contribution is a method for predicting the next step of the time-varying distribution from a given sequence of sample sets from earlier time steps. For this we rely on two recent machine learning techniques: embedding probability distributions into a reproducing kernel Hilbert space, and learning operators by vector-valued regression. We illustrate the working principles and the practical usefulness of our method by experiments on synthetic and real data. We also highlight an exemplary application: training a classifier in a domain adaptation setting without having access to examples from the test time distribution at training time."]]></description>
<dc:subject>to:NB prediction probability hilbert_space nonparametrics re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:aa1867d0c690/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2104.07798">
    <title>[2104.07798] Memory Order Decomposition of Symbolic Sequences</title>
    <dc:date>2021-04-19T14:39:06+00:00</dc:date>
    <link>https://arxiv.org/abs/2104.07798</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We introduce a general method for the study of memory in symbolic sequences based on higher-order Markov analysis. The Markov process that best represents a sequence is expressed as a mixture of matrices of minimal orders, enabling the definition of the so-called memory profile, which unambiguously reflects the true order of correlations. The method is validated by recovering the memory profiles of tunable synthetic sequences. Finally, we scan real data and showcase with practical examples how our protocol can be used to extract relevant stochastic properties of symbolic sequences."

--- Very interested to see if there's any mention of context trees, variable-order Markov chains, etc., let alone sofic processes.]]></description>
<dc:subject>to:NB to_read re:AoS_project markov_models latora.vito symbolic_dynamics color_me_skeptical</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:87b194c2d04a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:latora.vito"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:symbolic_dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:color_me_skeptical"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.mdpi.com/1099-4300/11/3/385">
    <title>Entropy | Free Full-Text | Properties of the Statistical Complexity Functional and Partially Deterministic HMMs</title>
    <dc:date>2020-05-16T17:46:39+00:00</dc:date>
    <link>https://www.mdpi.com/1099-4300/11/3/385</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Statistical complexity is a measure of complexity of discrete-time stationary stochastic processes, which has many applications. We investigate its more abstract properties as a non-linear function of the space of processes and show its close relation to the Knight’s prediction process. We prove lower semi-continuity, concavity, and a formula for the ergodic decomposition of statistical complexity. On the way, we show that the discrete version of the prediction process has a continuous Markov transition. We also prove that, given the past output of a partially deterministic hidden Markov model (HMM), the uncertainty of the internal state is constant over time and knowledge of the internal state gives no additional information on the future output. Using this fact, we show that the causal state distribution is the unique stationary representation on prediction space that may have finite entropy."]]></description>
<dc:subject>to:NB complexity_measures markov_models prediction stochastic_processes to_read re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7bbb0912fe69/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:complexity_measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1007.2075">
    <title>[1007.2075] Consistency of Feature Markov Processes</title>
    <dc:date>2020-05-16T17:45:18+00:00</dc:date>
    <link>https://arxiv.org/abs/1007.2075</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We are studying long term sequence prediction (forecasting). We approach this by investigating criteria for choosing a compact useful state representation. The state is supposed to summarize useful information from the history. We want a method that is asymptotically consistent in the sense it will provably eventually only choose between alternatives that satisfy an optimality property related to the used criterion. We extend our work to the case where there is side information that one can take advantage of and, furthermore, we briefly discuss the active setting where an agent takes actions to achieve desirable outcomes."]]></description>
<dc:subject>to:NB prediction hutter.marcus re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5586e9c8dc37/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hutter.marcus"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://escholarship.org/uc/item/25n8n5qb">
    <title>Modeling probability distributions with predictive state representations</title>
    <dc:date>2020-05-12T23:53:38+00:00</dc:date>
    <link>https://escholarship.org/uc/item/25n8n5qb</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This dissertation presents an in-depth analysis of the Predictive State Representation (PSR), a new model for sequence prediction. The key insight behind PSRs is that predictions of some possible future realizations of the sequence can be used to predict the probability of other possible futures. Previous work has shown PSRs are very flexible, and can be trained from data without many of the drawbacks of similar models. I present a rigorous theoretical foundation for understanding these models, and resolve several open problems in PSR theory. I also study multivariate prediction, where the model predicts the values of many random variables. The work presented in this dissertation is the first application of PSRs to modeling multivariate probability distributions. I also perform extensive comparisons of PSR learning algorithms against algorithms for learning other popular prediction models. Surprisingly, the comparisons are not always favorable to PSRs. My empirical results provide an important benchmark for future research on learning PSRs, and my theoretical results may aid development of better learning algorithms"]]></description>
<dc:subject>to:NB prediction to_read re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:fff1b9c46850/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.sciencedirect.com/science/article/abs/pii/S0031320305000233?via%3Dihub">
    <title>Links between probabilistic automata and hidden Markov models: probability distributions, learning models and induction algorithms - ScienceDirect</title>
    <dc:date>2020-05-12T23:51:32+00:00</dc:date>
    <link>https://www.sciencedirect.com/science/article/abs/pii/S0031320305000233?via%3Dihub</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This article presents an overview of Probabilistic Automata (PA) and discrete Hidden Markov Models (HMMs), and aims at clarifying the links between them. The first part of this work concentrates on probability distributions generated by these models. Necessary and sufficient conditions for an automaton to define a probabilistic language are detailed. It is proved that probabilistic deterministic automata (PDFA) form a proper subclass of probabilistic non-deterministic automata (PNFA). Two families of equivalent models are described next. On one hand, HMMs and PNFA with no final probabilities generate distributions over complete finite prefix-free sets. On the other hand, HMMs with final probabilities and probabilistic automata generate distributions over strings of finite length. The second part of this article presents several learning models, which formalize the problem of PA induction or, equivalently, the problem of HMM topology induction and parameter estimation. These learning models include the PAC and identification with probability 1 frameworks. Links with Bayesian learning are also discussed. The last part of this article presents an overview of induction algorithms for PA or HMMs using state merging, state splitting, parameter pruning and error-correcting techniques."]]></description>
<dc:subject>to:NB markov_models automata_theory to_read re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4432b2e40b08/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.100.208702">
    <title>Phys. Rev. Lett. 100, 208702 (2008) - Using the Memories of Multiscale Machines to Characterize Complex Systems</title>
    <dc:date>2020-05-12T23:50:33+00:00</dc:date>
    <link>https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.100.208702</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A scheme is presented to extract detailed dynamical signatures from successive measurements of complex systems. Relative entropy based time series tools are used to quantify the gain in predictive power of increasing past knowledge. By lossy compression, data is represented by increasingly coarsened symbolic strings. Each compression resolution is modeled by a machine: a finite memory transition matrix. Applying the relative entropy tools to each machine’s memory exposes correlations within many time scales. Examples are given for cardiac arrhythmias and different heart conditions are distinguished."]]></description>
<dc:subject>to:NB complexity_measures re:AoS_project to_read color_me_skeptical</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3ea37e3fcd80/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:complexity_measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:color_me_skeptical"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.mitpressjournals.org/doi/full/10.1162/neco.2009.10-08-878?casa_token=6OqPV0-CG1gAAAAA%3AnxxRJrjXQBD6YSskVxudW2fc7KH4hbzLAYkNOzRuOYdMEw3zNsJGfqpaef91YQ9jgpS0x95qgg">
    <title>Making the Error-Controlling Algorithm of Observable Operator Models Constructive | Neural Computation | MIT Press Journals</title>
    <dc:date>2020-05-12T23:49:41+00:00</dc:date>
    <link>https://www.mitpressjournals.org/doi/full/10.1162/neco.2009.10-08-878?casa_token=6OqPV0-CG1gAAAAA%3AnxxRJrjXQBD6YSskVxudW2fc7KH4hbzLAYkNOzRuOYdMEw3zNsJGfqpaef91YQ9jgpS0x95qgg</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Observable operator models (OOMs) are a class of models for stochastic processes that properly subsumes the class that can be modeled by finite-dimensional hidden Markov models (HMMs). One of the main advantages of OOMs over HMMs is that they admit asymptotically correct learning algorithms. A series of learning algorithms has been developed, with increasing computational and statistical efficiency, whose recent culmination was the error-controlling (EC) algorithm developed by the first author. The EC algorithm is an iterative, asymptotically correct algorithm that yields (and minimizes) an assured upper bound on the modeling error. The run time is faster by at least one order of magnitude than EM-based HMM learning algorithms and yields significantly more accurate models than the latter. Here we present a significant improvement of the EC algorithm: the constructive error-controlling (CEC) algorithm. CEC inherits from EC the main idea of minimizing an upper bound on the modeling error but is constructive where EC needs iterations. As a consequence, we obtain further gains in learning speed without loss in modeling accuracy."]]></description>
<dc:subject>to:NB to_read re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5d6c048b2f51/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/math/0606591">
    <title>[math/0606591] Approximation of stationary processes by Hidden Markov Models</title>
    <dc:date>2020-05-12T23:48:53+00:00</dc:date>
    <link>https://arxiv.org/abs/math/0606591</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We aim at the construction of a Hidden Markov Model (HMM) of assigned complexity (number of states of the underlying Markov chain) which best approximates, in Kullback-Leibler divergence rate, a given stationary process. We establish, under mild conditions, the existence of the divergence rate between a stationary process and an HMM. Since in general there is no analytic expression available for this divergence rate, we approximate it with a properly defined, and easily computable, divergence between Hankel matrices, which we use as our approximation criterion. We propose a three-step algorithm, based on the Nonnegative Matrix Factorization technique, which realizes an HMM optimal with respect to the defined approximation criterion. A full theoretical analysis of the algorithm is given in the special case of Markov approximation."]]></description>
<dc:subject>to:NB approximation stochastic_processes information_theory markov_models re:AoS_project to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7ded2a998ee1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/0912.4883">
    <title>[0912.4883] On Finding Predictors for Arbitrary Families of Processes</title>
    <dc:date>2020-05-12T23:47:12+00:00</dc:date>
    <link>https://arxiv.org/abs/0912.4883</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The problem is sequence prediction in the following setting. A sequence x1,...,xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) μ. After observing each outcome, it is required to give the conditional probabilities of the next observation. The measure μ belongs to an arbitrary but known class C of stochastic process measures. We are interested in predictors ρ whose conditional probabilities converge (in some sense) to the "true" μ-conditional probabilities if any μ∈C is chosen to generate the sequence. The contribution of this work is in characterizing the families C for which such predictors exist, and in providing a specific and simple form in which to look for a solution. We show that if any predictor works, then there exists a Bayesian predictor, whose prior is discrete, and which works too. We also find several sufficient and necessary conditions for the existence of a predictor, in terms of topological characterizations of the family C, as well as in terms of local behaviour of the measures in C, which in some cases lead to procedures for constructing such predictors. It should be emphasized that the framework is completely general: the stochastic processes considered are not required to be i.i.d., stationary, or to belong to any parametric or countable family."]]></description>
<dc:subject>to:NB prediction stochastic_processes to_read re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:309ca2e4e7df/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007%2Fs10994-008-5098-y">
    <title>Mining probabilistic automata: a statistical view of sequential pattern mining | SpringerLink</title>
    <dc:date>2020-05-12T23:45:35+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007%2Fs10994-008-5098-y</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["During the past decade, sequential pattern mining has been the core of numerous research efforts. It is now possible to efficiently extract knowledge of users’ behavior from a huge set of sequences collected over time. This has applications in various domains such as purchases in supermarkets, Web site visits, etc. However, sequence mining algorithms do little to control the risks of extracting false discoveries or overlooking true knowledge. In this paper, the theoretical conditions to achieve a relevant sequence mining process are examined. Then, the article offers a statistical view of sequence mining which has the following advantages: First, it uses a compact and generalized representation of the original sequences in the form of a probabilistic automaton. Second, it integrates statistical constraints to guarantee the extraction of significant patterns. Finally, it provides an interesting solution in a privacy preserving context in order to respect individuals’ information. An application in car flow modeling is presented, showing the ability of our algorithm (ACSM) to discover frequent routes without any private information. Comparisons with a classical sequence mining algorithm (SPAM) are made, showing the effectiveness of our approach."]]></description>
<dc:subject>to:NB to_read re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:16d9389f8c49/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/0902.2924">
    <title>[0902.2924] Model selection for weakly dependent time series forecasting</title>
    <dc:date>2020-05-12T23:43:43+00:00</dc:date>
    <link>https://arxiv.org/abs/0902.2924</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Observing a stationary time series, we propose a two-step procedure for the prediction of the next value of the time series. The first step follows machine learning theory paradigm and consists in determining a set of possible predictors as randomized estimators in (possibly numerous) different predictive models. The second step follows the model selection paradigm and consists in choosing one predictor with good properties among all the predictors of the first steps. We study our procedure for two different types of bservations: causal Bernoulli shifts and bounded weakly dependent processes. In both cases, we give oracle inequalities: the risk of the chosen predictor is close to the best prediction risk in all predictive models that we consider. We apply our procedure for predictive models such as linear predictors, neural networks predictors and non-parametric autoregressive."]]></description>
<dc:subject>have_read prediction model_selection time_series statistics to_teach:data_over_space_and_time re:AoS_project in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9db26429004d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:model_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data_over_space_and_time"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1002.0729">
    <title>[1002.0729] Minimal Markov Models</title>
    <dc:date>2020-05-12T23:43:09+00:00</dc:date>
    <link>https://arxiv.org/abs/1002.0729</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this work we introduce a new and richer class of finite order Markov chain models and address the following model selection problem: find the Markov model with the minimal set of parameters (minimal Markov model) which is necessary to represent a source as a Markov chain of finite order. Let us call M the order of the chain and A the finite alphabet, to determine the minimal Markov model, we define an equivalence relation on the state space AM, such that all the sequences of size M with the same transition probabilities are put in the same category. In this way we have one set of (|A|−1) transition probabilities for each category, obtaining a model with a minimal number of parameters. We show that the model can be selected consistently using the Bayesian information criterion."]]></description>
<dc:subject>to:NB to_read re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f41f4bc7b3d6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1005.5603">
    <title>[1005.5603] On the Relation between Realizable and Nonrealizable Cases of the Sequence Prediction Problem</title>
    <dc:date>2020-05-12T23:42:28+00:00</dc:date>
    <link>https://arxiv.org/abs/1005.5603</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A sequence x1,…,xn,… of discrete-valued observations is generated according to some unknown probabilistic law (measure) μ. After observing each outcome, one is required to give conditional probabilities of the next observation. The realizable case is when the measure μ belongs to an arbitrary but known class  of process measures. The non-realizable case is when μ is completely arbitrary, but the prediction performance is measured with respect to a given set  of process measures. We are interested in the relations between these problems and between their solutions, as well as in characterizing the cases when a solution exists and finding these solutions. We show that if the quality of prediction is measured using the total variation distance, then these problems coincide, while if it is measured using the expected average KL divergence, then they are different. For some of the formalizations we also show that when a solution exists, it can be obtained as a Bayes mixture over a countable subset of . We also obtain several characterization of those sets  for which solutions to the considered problems exist. As an illustration to the general results obtained, we show that a solution to the non-realizable case of the sequence prediction problem exists for the set of all finite-memory processes, but does not exist for the set of all stationary processes.
"It should be emphasized that the framework is completely general: the processes measures considered are not required to be i.i.d., mixing, stationary, or to belong to any parametric family."]]></description>
<dc:subject>to:NB prediction to_read re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d1b26bbbdc24/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.mitpressjournals.org/doi/full/10.1162/neco.2010.03-09-983?casa_token=Wtos_gRuXBwAAAAA%3ASF00100yV26d79wv_ZqPJXdvYugtmxs_DCSq3qObsT7eebCxfCI5fZL-eDfPtnf-vcXywIg17w">
    <title>Norm-Observable Operator Models | Neural Computation | MIT Press Journals</title>
    <dc:date>2020-05-12T23:41:00+00:00</dc:date>
    <link>https://www.mitpressjournals.org/doi/full/10.1162/neco.2010.03-09-983?casa_token=Wtos_gRuXBwAAAAA%3ASF00100yV26d79wv_ZqPJXdvYugtmxs_DCSq3qObsT7eebCxfCI5fZL-eDfPtnf-vcXywIg17w</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Hidden Markov models (HMMs) are one of the most popular and successful statistical models for time series. Observable operator models (OOMs) are generalizations of HMMs that exhibit several attractive advantages. In particular, a variety of highly efficient, constructive, and asymptotically correct learning algorithms are available for OOMs. However, the OOM theory suffers from the negative probability problem (NPP): a given, learned OOM may sometimes predict negative probabilities for certain events. It was recently shown that it is undecidable whether a given OOM will eventually produce such negative values.
"We propose a novel variant of OOMs, called norm-observable operator models (NOOMs), which avoid the NPP by design. Like OOMs, NOOMs use a set of linear operators to update system states. But differing from OOMs, they represent probabilities by the square of the norm of system states, thus precluding negative probability values. While being free of the NPP, NOOMs retain most advantages of OOMs. For example, NOOMs also capture (some) processes that cannot be modeled by HMMs. More importantly, in principle, NOOMs can be learned from data in a constructive way, and the learned models are asymptotically correct. We also prove that NOOMs capture all Markov chain (MC) describable processes.
"This letter presents the mathematical foundations of NOOMs, discusses the expressiveness of the model class, and explains how a NOOM can be estimated from data constructively."]]></description>
<dc:subject>to:NB to_read re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:84a69b274394/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1206.2691">
    <title>[1206.2691] IDS: An Incremental Learning Algorithm for Finite Automata</title>
    <dc:date>2020-05-12T23:39:52+00:00</dc:date>
    <link>https://arxiv.org/abs/1206.2691</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present a new algorithm IDS for incremental learning of deterministic finite automata (DFA). This algorithm is based on the concept of distinguishing sequences introduced in (Angluin81). We give a rigorous proof that two versions of this learning algorithm correctly learn in the limit. Finally we present an empirical performance analysis that compares these two algorithms, focussing on learning times and different types of learning queries. We conclude that IDS is an efficient algorithm for software engineering applications of automata learning, such as testing and model inference."]]></description>
<dc:subject>to:NB automata_theory to_read re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:df50716e49d4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/how-many-future-measures-can-there-be/10B4CABB6000B5D78264000C8792B011">
    <title>How many future measures can there be? | Ergodic Theory and Dynamical Systems | Cambridge Core</title>
    <dc:date>2020-05-12T23:38:39+00:00</dc:date>
    <link>https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/how-many-future-measures-can-there-be/10B4CABB6000B5D78264000C8792B011</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The question addressed in this paper is the worst-case growth rate, for ergodic processes, in the number of conditional measures on n-steps in the future, given the past, that are a fixed distance apart. It is shown that if error is measured using the variational (i.e. distributional) distance then doubly exponential growth is possible, while if error is measured using the \bar{d}-metric then more than exponential growth is possible. The question of whether doubly exponential growth is possible in the \bar{d}case is left open."]]></description>
<dc:subject>to:NB stochastic_processes prediction re:AoS_project to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:10aa8a4d5e59/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.sciencedirect.com/science/article/pii/S0304397501002717">
    <title>Determinization of transducers over finite and infinite words - ScienceDirect</title>
    <dc:date>2020-05-12T23:37:41+00:00</dc:date>
    <link>https://www.sciencedirect.com/science/article/pii/S0304397501002717</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study the determinization of transducers over finite and infinite words. The first part of the paper is devoted to finite words. We recall the characterization of subsequential functions due to Choffrut. We describe here a known algorithm to determinize a transducer.
"In the case of infinite words, we consider transducers with all their states final. We give an effective characterization of sequential functions over infinite words. We describe an algorithm to determinize transducers over infinite words. This part contains the main novel results of the paper."]]></description>
<dc:subject>to:NB to_read automata_theory re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a37e5b271ed4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1005.2263">
    <title>[1005.2263] Context models on sequences of covers</title>
    <dc:date>2020-05-12T23:36:37+00:00</dc:date>
    <link>https://arxiv.org/abs/1005.2263</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the conditioning variable and maintaining a different model for each set within a cover. Inference remains tractable by specifying the probabilistic model in terms of a random walk within the sequence of covers. We demonstrate the approach on problems of conditional density estimation, which, to our knowledge is the first closed-form, non-parametric Bayesian approach to this problem."]]></description>
<dc:subject>to:NB to_read re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:61e6c7f6ceb4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/s11009-019-09706-8">
    <title>Stochastic Analysis of Minimal Automata Growth for Generalized Strings | SpringerLink</title>
    <dc:date>2020-02-23T15:36:47+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s11009-019-09706-8</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Generalized strings describe various biological motifs that arise in molecular and computational biology. In this manuscript, we introduce an alternative but efficient algorithm to construct the minimal deterministic finite automaton (DFA) associated with any generalized string. We exploit this construction to characterize the typical growth of the minimal DFA (i.e., with the least number of states) associated with a random generalized string of increasing length. Even though the worst-case growth may be exponential, we characterize a point in the construction of the minimal DFA when it starts to grow linearly and conclude it has at most a polynomial number of states with asymptotically certain probability. We conjecture that this number is linear."]]></description>
<dc:subject>to:NB automata_theory re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:195833fbbd8f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.12243">
    <title>[1909.12243] Data Smashing 2.0: Sequence Likelihood (SL) Divergence For Fast Time Series Comparison</title>
    <dc:date>2019-10-01T17:26:45+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.12243</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Recognizing subtle historical patterns is central to modeling and forecasting problems in time series analysis. Here we introduce and develop a new approach to quantify deviations in the underlying hidden generators of observed data streams, resulting in a new efficiently computable universal metric for time series. The proposed metric is in the sense that we can compare and contrast data streams regardless of where and how they are generated and without any feature engineering step. The approach proposed in this paper is conceptually distinct from our previous work on data smashing, and vastly improves discrimination performance and computing speed. The core idea here is the generalization of the notion of KL divergence often used to compare probability distributions to a notion of divergence in time series. We call this the sequence likelihood (SL) divergence, which may be used to measure deviations within a well-defined class of discrete-valued stochastic processes. We devise efficient estimators of SL divergence from finite sample paths and subsequently formulate a universal metric useful for computing distance between time series produced by hidden stochastic generators."

--- If this is just the divergence rate, I'll cry.

--- ETA after skimming: Not only is it the divergence rate, they're using the (obvious) expression to calculate it from predictive state representations, and their inference algorithm for same is either CSSR or very, very close.  I feel simultaneously gratified and nonplussed. ]]></description>
<dc:subject>to:NB time_series statistics information_theory have_skimmed re:AoS_project color_me_skeptical</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9e590814f26e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_skimmed"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:color_me_skeptical"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1908.06240">
    <title>[1908.06240] Markov chains with exponential return times are finitary</title>
    <dc:date>2019-08-20T14:49:05+00:00</dc:date>
    <link>https://arxiv.org/abs/1908.06240</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Consider an ergodic Markov chain on a countable state space for which the return times have exponential tails. We show that the stationary version of any such chain is a finitary factor of an i.i.d. process. A key step is to show that any stationary renewal process whose jump distribution has exponential tails and is not supported on a proper subgroup of ℤ is a finitary factor of an i.i.d. process."]]></description>
<dc:subject>to:NB markov_models re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f0a8c361319f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1905.12262">
    <title>[1905.12262] Flexible Mining of Prefix Sequences from Time-Series Traces</title>
    <dc:date>2019-05-30T16:15:40+00:00</dc:date>
    <link>https://arxiv.org/abs/1905.12262</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Mining temporal assertions from time-series data using information theory to filter real properties from incidental ones is a practically significant challenge. The problem is complex for continuous or hybrid systems because the degrees of influence on a consequent from a timed-sequence of predicates (called its prefix sequence), varies continuously over dense time intervals. We propose a parameterized method that uses interval arithmetic for flexibly learning prefix sequences having influence on a defined consequent over various time scales and predicates over system variables."]]></description>
<dc:subject>prediction time_series re:AoS_project variable-length_markov_models_aka_context_trees in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d9b2c25a321a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variable-length_markov_models_aka_context_trees"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.mitpressjournals.org/doi/abs/10.1162/neco_a_01101">
    <title>A Locally Optimal Algorithm for Estimating a Generating Partition from an Observed Time Series and Its Application to Anomaly Detection | Neural Computation | MIT Press Journals</title>
    <dc:date>2018-10-11T17:45:37+00:00</dc:date>
    <link>https://www.mitpressjournals.org/doi/abs/10.1162/neco_a_01101</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Estimation of a generating partition is critical for symbolization of measurements from discrete-time dynamical systems, where a sequence of symbols from a (finite-cardinality) alphabet may uniquely specify the underlying time series. Such symbolization is useful for computing measures (e.g., Kolmogorov-Sinai entropy) to identify or characterize the (possibly unknown) dynamical system. It is also useful for time series classification and anomaly detection. The seminal work of Hirata, Judd, and Kilminster (2004) derives a novel objective function, akin to a clustering objective, that measures the discrepancy between a set of reconstruction values and the points from the time series. They cast estimation of a generating partition via the minimization of their objective function. Unfortunately, their proposed algorithm is nonconvergent, with no guarantee of finding even locally optimal solutions with respect to their objective. The difficulty is a heuristic nearest neighbor symbol assignment step. Alternatively, we develop a novel, locally optimal algorithm for their objective. We apply iterative nearest-neighbor symbol assignments with guaranteed discrepancy descent, by which joint, locally optimal symbolization of the entire time series is achieved. While most previous approaches frame generating partition estimation as a state-space partitioning problem, we recognize that minimizing the Hirata et al. (2004) objective function does not induce an explicit partitioning of the state space, but rather the space consisting of the entire time series (effectively, clustering in a (countably) infinite-dimensional space). Our approach also amounts to a novel type of sliding block lossy source coding. Improvement, with respect to several measures, is demonstrated over popular methods for symbolizing chaotic maps. We also apply our approach to time-series anomaly detection, considering both chaotic maps and failure application in a polycrystalline alloy material."]]></description>
<dc:subject>time_series symbolic_dynamics information_theory re:AoS_project in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3cc585677811/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:symbolic_dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.sciencedirect.com/science/article/pii/S0020019011003267">
    <title>Fast brief practical DFA minimization - ScienceDirect</title>
    <dc:date>2018-10-06T17:31:40+00:00</dc:date>
    <link>https://www.sciencedirect.com/science/article/pii/S0020019011003267</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Minimization of deterministic finite automata has traditionally required complicated programs and correctness proofs, and taken 
 time, where n is the number of states and k the size of the alphabet. Here a short, memory-efficient program is presented that runs in 
, or even in 
, time, where m is the number of transitions. The program is complete with input, output, and the removal of irrelevant parts of the automaton. Its invariant-style correctness proof is relatively short."]]></description>
<dc:subject>automata_theory re:AoS_project to_read via:? in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b903883a5614/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:?"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00898#.WH0fKbGZOL8">
    <title>On the Mathematical Consequences of Binning Spike Trains | Neural Computation | MIT Press Journals</title>
    <dc:date>2017-01-16T19:39:24+00:00</dc:date>
    <link>http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00898#.WH0fKbGZOL8</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We initiate a mathematical analysis of hidden effects induced by binning spike trains of neurons. Assuming that the original spike train has been generated by a discrete Markov process, we show that binning generates a stochastic process that is no longer Markov but is instead a variable-length Markov chain (VLMC) with unbounded memory. We also show that the law of the binned raster is a Gibbs measure in the DLR (Dobrushin-Lanford-Ruelle) sense coined in mathematical statistical mechanics. This allows the derivation of several important consequences on statistical properties of binned spike trains. In particular, we introduce the DLR framework as a natural setting to mathematically formalize anticipation, that is, to tell “how good” our nervous system is at making predictions. In a probabilistic sense, this corresponds to condition a process by its future, and we discuss how binning may affect our conclusions on this ability. We finally comment on the possible consequences of binning in the detection of spurious phase transitions or in the detection of incorrect evidence of criticality."]]></description>
<dc:subject>to:NB neural_data_analysis stochastic_processes binning information_theory markov_models chains_with_complete_connections re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bb78899ef3b6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:binning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:chains_with_complete_connections"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.jmlr.org/papers/v16/thon15a.html">
    <title>Links Between Multiplicity Automata, Observable Operator Models and Predictive State Representations -- a Unified Learning Framework</title>
    <dc:date>2016-11-30T02:09:54+00:00</dc:date>
    <link>http://www.jmlr.org/papers/v16/thon15a.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Stochastic multiplicity automata (SMA) are weighted finite automata that generalize probabilistic automata. They have been used in the context of probabilistic grammatical inference. Observable operator models (OOMs) are a generalization of hidden Markov models, which in turn are models for discrete-valued stochastic processes and are used ubiquitously in the context of speech recognition and bio-sequence modeling. Predictive state representations (PSRs) extend OOMs to stochastic input-output systems and are employed in the context of agent modeling and planning.
"We present SMA, OOMs, and PSRs under the common framework of sequential systems, which are an algebraic characterization of multiplicity automata, and examine the precise relationships between them. Furthermore, we establish a unified approach to learning such models from data. Many of the learning algorithms that have been proposed can be understood as variations of this basic learning scheme, and several turn out to be closely related to each other, or even equivalent."]]></description>
<dc:subject>to:NB re:AoS_project stochastic_processes statistics prediction state-space_models automata_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:25727a8ab045/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1204.2477">
    <title>[1204.2477] A Simple Explanation of A Spectral Algorithm for Learning Hidden Markov Models</title>
    <dc:date>2016-11-30T01:58:35+00:00</dc:date>
    <link>https://arxiv.org/abs/1204.2477</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A simple linear algebraic explanation of the algorithm in "A Spectral Algorithm for Learning Hidden Markov Models" (COLT 2009). Most of the content is in Figure 2; the text just makes everything precise in four nearly-trivial claims."]]></description>
<dc:subject>to:NB spectral_methods re:AoS_project markov_models state-space_models statistics time_series estimation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:384a791646c5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spectral_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://ieeexplore.ieee.org/abstract/document/7560625/">
    <title>Optimal Code Length Estimates from Dependent Samples with Bounds on the Estimation Error - IEEE Xplore Document</title>
    <dc:date>2016-11-24T21:08:37+00:00</dc:date>
    <link>http://ieeexplore.ieee.org/abstract/document/7560625/</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Modern communication networks require robust and adaptive communication protocols to optimize various performance metrics like latency and energy efficiency. Adaptive communication protocols require real-time estimation of critical system parameters, amongst which the average length of an optimal source code is of key importance, when data compression is involved. In this letter, we prove finite-sample estimates— along with their confidence levels—of the worst-case average length of an optimal source code over a channel transmitting dependent data. More specifically, this is achieved by establishing a concentration inequality for the estimation of entropy of the source. Data dependence is modelled through stationary mixing. Evaluation of the proposed bounds is computationally efficient and can be used for real-time estimation."]]></description>
<dc:subject>information_theory entropy_estimation statistics re:AoS_project in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d1177e7f2375/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entropy_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.cs.nyu.edu/~mohri/postscript/jnle.ps">
    <title>On Some Applications of Finite-State Automata Theory to Natural Language Processing</title>
    <dc:date>2016-03-31T11:41:30+00:00</dc:date>
    <link>http://www.cs.nyu.edu/~mohri/postscript/jnle.ps</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>to:NB automata_theory natural_language_processing re:AoS_project mohri.mehryar</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:26242092ca42/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:natural_language_processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mohri.mehryar"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.cs.nyu.edu/~mohri/pub/finite.ps">
    <title>Finitely subsequential transducers</title>
    <dc:date>2016-03-31T11:40:15+00:00</dc:date>
    <link>http://www.cs.nyu.edu/~mohri/pub/finite.ps</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>to:NB to_read automata_theory mohri.meryar re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e4c3ad7a0434/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mohri.meryar"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.aop/1176996452">
    <title>Freedman : On Tail Probabilities for Martingales</title>
    <dc:date>2016-02-06T21:02:18+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.aop/1176996452</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Watch a martingale with uniformly bounded increments until it first crosses the horizontal line of height $a$. The sum of the conditional variances of the increments given the past, up to the crossing, is an intrinsic measure of the crossing time. Simple and fairly sharp upper and lower bounds are given for the Laplace transform of this crossing time, which show that the distribution is virtually the same as that for the crossing time of Brownian motion, even in the tail. The argument can be adapted to extend inequalities of Bernstein and Kolmogorov to the dependent case, proving the law of the iterated logarithm for martingales. The argument can also be adapted to prove Levy's central limit theorem for martingales. The results can be extended to martingales whose increments satisfy a growth condition."]]></description>
<dc:subject>deviation_inequalities martingales probability re:AoS_project in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b0ba442773d1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:deviation_inequalities"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:martingales"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1304.5774">
    <title>[1304.5774] On the probability of being synchronizable</title>
    <dc:date>2015-12-01T21:47:54+00:00</dc:date>
    <link>http://arxiv.org/abs/1304.5774</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We prove that a random automaton with n states and any fixed non-singleton alphabet is synchronizing with high probability. Moreover, we also prove that the convergence rate is exactly 1−Θ(1/n) as conjectured by Cameron \cite{CamConj} for the most interesting binary alphabet case."]]></description>
<dc:subject>automata_theory synchronizing_words re:AoS_project via:vaguery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1a94e1ac1b18/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:synchronizing_words"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:vaguery"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1506.04513">
    <title>[1506.04513] Convex Risk Minimization and Conditional Probability Estimation</title>
    <dc:date>2015-07-14T09:40:20+00:00</dc:date>
    <link>http://arxiv.org/abs/1506.04513</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general enough to include cases in which no minimum exists, as occurs typically, for instance, with standard boosting algorithms. Concretely, we first show that any sequence of predictors minimizing convex risk over the source distribution will converge to this unique model when the class of predictors is linear (but potentially of infinite dimension). Secondly, we show the same result holds for \emph{empirical} risk minimization whenever this class of predictors is finite dimensional, where the essential technical contribution is a norm-free generalization bound."]]></description>
<dc:subject>to:NB learning_theory statistics density_estimation re:AoS_project to_teach:childs_garden_of_statistical_learning_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6897d617cff8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:childs_garden_of_statistical_learning_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1505.05310">
    <title>[1505.05310] A New View of Predictive State Methods for Dynamical System Learning</title>
    <dc:date>2015-06-05T03:11:26+00:00</dc:date>
    <link>http://arxiv.org/abs/1505.05310</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Recently there has been substantial interest in predictive state methods for learning dynamical systems: these algorithms are popular since they often offer a good tradeoff between computational speed and statistical efficiency. Despite their desirable properties, though, predictive state methods can sometimes be difficult to use in practice. E.g., in contrast to the rich literature on supervised learning methods, which allows us to choose from an extensive menu of models and algorithms to suit the prior beliefs we have about properties of the function to be learned, predictive state dynamical system learning methods are comparatively inflexible: it is as if we were restricted to use only linear regression instead of being allowed to choose decision trees, nonparametric regression, or the lasso. To address this problem, we propose a new view of predictive state methods in terms of instrumental variable regression. This view allows us to construct a wide variety of dynamical system learners simply by swapping in different supervised learning methods. We demonstrate the effectiveness of our proposed methods by experimenting with non-linear regression to learn a hidden Markov model, showing that the resulting algorithm outperforms the correctness of this algorithm follows directly from our general analysis."]]></description>
<dc:subject>to_read re:AoS_project gordon.geoff in_NB predictive_states</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8753bfa934ba/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:gordon.geoff"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:predictive_states"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.aoms/1177699065">
    <title>Skibinsky : Adequate Subfields and Sufficiency</title>
    <dc:date>2015-05-09T23:39:53+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.aoms/1177699065</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>to_read sufficiency statistics re:AoS_project prediction in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:29bdb88a8146/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sufficiency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1411.7650">
    <title>[1411.7650] Nonparametric statistical inference for the context tree of a stationary ergodic process</title>
    <dc:date>2015-01-20T04:00:15+00:00</dc:date>
    <link>http://arxiv.org/abs/1411.7650</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider the problem of estimating the context tree of a stationary ergodic process with finite alphabet without imposing additional conditions on the processes. As a starting point we introduce a Hamming metric in the space of irreducible context trees and we use the properties of the weak topology in the space of ergodic stationary processes to prove that if the Hamming metric is unbounded, there exist no consistent estimators for the context tree. Even in the bounded case we show that there exist no two-sided confidence bounds. However we prove that one-sided inference is possible in this general setting and we construct a consistent estimator that is a lower bound for the context tree of the process with an explicit formula for the coverage probability."]]></description>
<dc:subject>statistics statistical_inference_for_stochastic_processes ergodic_theory prediction re:AoS_project confidence_sets variable-length_markov_models_aka_context_trees have_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7ff1521daee5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:confidence_sets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variable-length_markov_models_aka_context_trees"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1501.01300">
    <title>[1501.01300] Computational Complexity of the Minimum State Probabilistic Finite State Learning Problem on Finite Data Sets</title>
    <dc:date>2015-01-13T13:50:15+00:00</dc:date>
    <link>http://arxiv.org/abs/1501.01300</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we study the problem of determining a minimum state probabilistic finite state machine capable of generating statistically identical symbol sequences to samples provided. This problem is qualitatively similar to the classical Hidden Markov Model problem and has been studied from a practical point of view in several works beginning with the work presented in: Shalizi, C.R., Shalizi, K.L., Crutchfield, J.P. (2002) [arXiv:cs/0210025]. In this paper, we show that the underlying problem is NP-hard and thus all existing polynomial time algorithms must be approximations on finite data sets. Using our NP-hardness proof, we show how to construct a provably correct algorithm for constructing a minimum state probabilistic finite state machine given data and empirically study its running time."

--- Huh, didn't we show that CSSR has worst-case exponential time, and was just quadratic _on average_?  Anyway, clearly needs to be read.]]></description>
<dc:subject>to:NB to_read theoretical_computer_science automata_theory markov_models re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:71480c8cc587/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:theoretical_computer_science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.pnas.org/content/111/41/14651.abstract.html?etoc">
    <title>On inference of causality for discrete state models in a multiscale context</title>
    <dc:date>2014-10-18T02:52:12+00:00</dc:date>
    <link>http://www.pnas.org/content/111/41/14651.abstract.html?etoc</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Discrete state models are a common tool of modeling in many areas. E.g., Markov state models as a particular representative of this model family became one of the major instruments for analysis and understanding of processes in molecular dynamics (MD). Here we extend the scope of discrete state models to the case of systematically missing scales, resulting in a nonstationary and nonhomogeneous formulation of the inference problem. We demonstrate how the recently developed tools of nonstationary data analysis and information theory can be used to identify the simultaneously most optimal (in terms of describing the given data) and most simple (in terms of complexity and causality) discrete state models. We apply the resulting formalism to a problem from molecular dynamics and show how the results can be used to understand the spatial and temporal causality information beyond the usual assumptions. We demonstrate that the most optimal explanation for the appropriately discretized/coarse-grained MD torsion angles data in a polypeptide is given by the causality that is localized both in time and in space, opening new possibilities for deploying percolation theory and stochastic subgridscale modeling approaches in the area of MD."]]></description>
<dc:subject>to:NB to_read re:AoS_project time_series markov_models statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1fc0a8eb9f01/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.aos/1018031110">
    <title>Nobel : Limits to classification and regression estimation from ergodic processes</title>
    <dc:date>2014-08-07T16:06:36+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.aos/1018031110</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We answer two open questions concerning the existence of universal schemes for classification and regression estimation from stationary ergodic processes. It is shown that no measurable procedure can produce weakly consistent regression estimates from every bivariate stationary ergodic process, even if the covariate and response variables are restricted to take values in the unit interval. It is further shown that no measurable procedure can produce weakly consistent classification rules from every bivariate stationary ergodic process for which the response variable is binary valued. The results of the paper are derived via reduction arguments and are based in part on recent work concerning density estimaton from ergodic processes."]]></description>
<dc:subject>to_read ergodic_theory classifiers regression learning_theory statistics have_read have_forgotten re:AoS_project nobel.andrew in_NB to_teach:childs_garden_of_statistical_learning_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:745ac5dff27e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:classifiers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_forgotten"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nobel.andrew"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:childs_garden_of_statistical_learning_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://link.springer.com/article/10.1007/s10994-013-5416-x?wt_mc=alerts.TOCjournals">
    <title>Spectral learning of weighted automata - Springer</title>
    <dc:date>2014-07-31T14:51:43+00:00</dc:date>
    <link>http://link.springer.com/article/10.1007/s10994-013-5416-x?wt_mc=alerts.TOCjournals</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In recent years we have seen the development of efficient provably correct algorithms for learning Weighted Finite Automata (WFA). Most of these algorithms avoid the known hardness results by defining parameters beyond the number of states that can be used to quantify the complexity of learning automata under a particular distribution. One such class of methods are the so-called spectral algorithms that measure learning complexity in terms of the smallest singular value of some Hankel matrix. However, despite their simplicity and wide applicability to real problems, their impact in application domains remains marginal to this date. One of the goals of this paper is to remedy this situation by presenting a derivation of the spectral method for learning WFA that—without sacrificing rigor and mathematical elegance—puts emphasis on providing intuitions on the inner workings of the method and does not assume a strong background in formal algebraic methods. In addition, our algorithm overcomes some of the shortcomings of previous work and is able to learn from statistics of substrings. To illustrate the approach we present experiments on a real application of the method to natural language parsing."]]></description>
<dc:subject>to:NB to_read re:AoS_project spectral_methods automata_theory grammar_induction markov_models state-space_models learning_theory machine_learning statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d678b734bce5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spectral_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:grammar_induction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://link.springer.com/article/10.1007/s10994-013-5408-x?wt_mc=alerts.TOCjournals">
    <title>Adaptively learning probabilistic deterministic automata from data streams - Springer</title>
    <dc:date>2014-07-31T14:50:44+00:00</dc:date>
    <link>http://link.springer.com/article/10.1007/s10994-013-5408-x?wt_mc=alerts.TOCjournals</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Markovian models with hidden state are widely-used formalisms for modeling sequential phenomena. Learnability of these models has been well studied when the sample is given in batch mode, and algorithms with PAC-like learning guarantees exist for specific classes of models such as Probabilistic Deterministic Finite Automata (PDFA). Here we focus on PDFA and give an algorithm for inferring models in this class in the restrictive data stream scenario: Unlike existing methods, our algorithm works incrementally and in one pass, uses memory sublinear in the stream length, and processes input items in amortized constant time. We also present extensions of the algorithm that (1) reduce to a minimum the need for guessing parameters of the target distribution and (2) are able to adapt to changes in the input distribution, relearning new models when needed. We provide rigorous PAC-like bounds for all of the above. Our algorithm makes a key usage of stream sketching techniques for reducing memory and processing time, and is modular in that it can use different tests for state equivalence and for change detection in the stream."]]></description>
<dc:subject>to:NB to_read re:AoS_project grammar_induction markov_models state-space_models automata_theory machine_learning statistics learning_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8f5ba4f6e75b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:grammar_induction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://link.springer.com/article/10.1007/s10994-013-5409-9?wt_mc=alerts.TOCjournals">
    <title>PAutomaC: a probabilistic automata and hidden Markov models learning competition - Springer</title>
    <dc:date>2014-07-31T14:49:51+00:00</dc:date>
    <link>http://link.springer.com/article/10.1007/s10994-013-5409-9?wt_mc=alerts.TOCjournals</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Approximating distributions over strings is a hard learning problem. Typical techniques involve using finite state machines as models and attempting to learn these; these machines can either be hand built and then have their weights estimated, or built by grammatical inference techniques: the structure and the weights are then learned simultaneously. The Probabilistic Automata learning Competition (PAutomaC), run in 2012, was the first grammatical inference challenge that allowed the comparison between these methods and algorithms. Its main goal was to provide an overview of the state-of-the-art techniques for this hard learning problem. Both artificial data and real data were presented and contestants were to try to estimate the probabilities of strings. The purpose of this paper is to describe some of the technical and intrinsic challenges such a competition has to face, to give a broad state of the art concerning both the problems dealing with learning grammars and finite state machines and the relevant literature. This paper also provides the results of the competition and a brief description and analysis of the different approaches the main participants used."]]></description>
<dc:subject>to:NB to_read re:AoS_project grammar_induction markov_models state-space_models machine_learning</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:42c98a8f6199/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:grammar_induction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.ams.org/samplings/math-history/hmbrowder-diaconis.pdf">
    <title>Sufficiency as Statistical Symmetry</title>
    <dc:date>2014-07-22T17:32:41+00:00</dc:date>
    <link>http://www.ams.org/samplings/math-history/hmbrowder-diaconis.pdf</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>sufficiency statistics symmetry mathematics diaconis.persi have_read track_down_references re:AoS_project in_NB to:blog</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bc9a8a685418/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sufficiency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:diaconis.persi"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:track_down_references"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:blog"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.ma.utexas.edu/mp_arc/c/05/05-65.pdf">
    <title>Concentration Inequalities and Estimation of Conditional Probabilities</title>
    <dc:date>2014-06-14T14:08:29+00:00</dc:date>
    <link>https://www.ma.utexas.edu/mp_arc/c/05/05-65.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We prove concentration inequalities inspired from [DP] to obtain estimators of conditional probabilities for weak dependant se- quences. This generalize results from Csisza ́r ([Cs]). For Gibbs mea- sures and dynamical systems, these results lead to construct estimators of the potential function and also to test the nullity of the asymptotic variance of the system."]]></description>
<dc:subject>concentration_of_measure stochastic_processes re:AoS_project have_read mixing in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4ae738278aa9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:concentration_of_measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://jmlr.org/proceedings/papers/v33/kulesza14.html">
    <title>Low-Rank Spectral Learning | AISTATS 2014 | JMLR W&amp;CP</title>
    <dc:date>2014-04-20T17:47:44+00:00</dc:date>
    <link>http://jmlr.org/proceedings/papers/v33/kulesza14.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Spectral learning methods have recently been proposed as alternatives to slow, non-convex optimization algorithms like EM for a variety of probabilistic models in which hidden information must be inferred by the learner. These methods are typically controlled by a rank hyperparameter that sets the complexity of the model; when the model rank matches the true rank of the process generating the data, the resulting predictions are provably consistent and admit finite sample convergence bounds. However, in practice we usually do not know the true rank, and, in any event, from a computational and statistical standpoint it is likely to be prohibitively large. It is therefore of great practical interest to understand the behavior of low-rank spectral learning, where the model rank is less than the true rank. Counterintuitively, we show that even when the singular values omitted by lowering the rank are arbitrarily small, the resulting prediction errors can in fact be arbitrarily large. We identify two distinct possible causes for this bad behavior, and illustrate them with simple examples. We then show that these two causes are essentially complete: assuming that they do not occur, we can prove that the prediction error is bounded in terms of the magnitudes of the omitted singular values. We argue that the assumptions necessary for this result are relatively realistic, making low-rank spectral learning a viable option for many applications."]]></description>
<dc:subject>to:NB spectral_methods low-rank_approximation statistics computational_statistics principal_components re:AoS_project singh.satinder_baveja</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:273a202b361f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spectral_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:low-rank_approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:singh.satinder_baveja"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1401.3870">
    <title>[1401.3870] Learning to Make Predictions In Partially Observable Environments Without a Generative Model</title>
    <dc:date>2014-03-10T18:04:11+00:00</dc:date>
    <link>http://arxiv.org/abs/1401.3870</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["When faced with the problem of learning a model of a high-dimensional environment, a common approach is to limit the model to make only a restricted set of predictions, thereby simplifying the learning problem. These partial models may be directly useful for making decisions or may be combined together to form a more complete, structured model. However, in partially observable (non-Markov) environments, standard model-learning methods learn generative models, i.e. models that provide a probability distribution over all possible futures (such as POMDPs). It is not straightforward to restrict such models to make only certain predictions, and doing so does not always simplify the learning problem. In this paper we present prediction profile models: non-generative partial models for partially observable systems that make only a given set of predictions, and are therefore far simpler than generative models in some cases. We formalize the problem of learning a prediction profile model as a transformation of the original model-learning problem, and show empirically that one can learn prediction profile models that make a small set of important predictions even in systems that are too complex for standard generative models."]]></description>
<dc:subject>to:NB prediction inference_to_latent_objects statistics singh.satinder_baveja to_read re:AoS_project control_theory_and_control_engineering</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3a5123b51734/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:inference_to_latent_objects"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:singh.satinder_baveja"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1401.0742">
    <title>[1401.0742] Data Smashing</title>
    <dc:date>2014-03-10T02:14:47+00:00</dc:date>
    <link>http://arxiv.org/abs/1401.0742</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Investigation of the underlying physics or biology from empirical data requires a quantifiable notion of similarity - when do two observed data sets indicate nearly identical generating processes, and when they do not. The discriminating characteristics to look for in data is often determined by heuristics designed by experts, e.g., distinct shapes of "folded" lightcurves may be used as "features" to classify variable stars, while determination of pathological brain states might require a Fourier analysis of brainwave activity. Finding good features is non-trivial. Here, we propose a universal solution to this problem: we delineate a principle for quantifying similarity between sources of arbitrary data streams, without a priori knowledge, features or training. We uncover an algebraic structure on a space of symbolic models for quantized data, and show that such stochastic generators may be added and uniquely inverted; and that a model and its inverse always sum to the generator of flat white noise. Therefore, every data stream has an anti-stream: data generated by the inverse model. Similarity between two streams, then, is the degree to which one, when summed to the other's anti-stream, mutually annihilates all statistical structure to noise. We call this data smashing. We present diverse applications, including disambiguation of brainwaves pertaining to epileptic seizures, detection of anomalous cardiac rhythms, and classification of astronomical objects from raw photometry. In our examples, the data smashing principle, without access to any domain knowledge, meets or exceeds the performance of specialized algorithms tuned by domain experts."]]></description>
<dc:subject>to:NB data_analysis statistics stochastic_processes lipson.hod re:AoS_project color_me_skeptical</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:677dfc46524a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lipson.hod"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:color_me_skeptical"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1401.0711">
    <title>[1401.0711] Computing Entropy Rate Of Symbol Sources &amp; A Distribution-free Limit Theorem</title>
    <dc:date>2014-03-10T02:11:59+00:00</dc:date>
    <link>http://arxiv.org/abs/1401.0711</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be carried out without explicit background noise characterization. However, state of the art algorithms to estimate the entropy rate have markedly slow convergence; making such entropic approaches non-viable in practice. We present here a fundamentally new approach to estimate entropy rates, which is demonstrated to converge significantly faster in terms of input data lengths, and is shown to be effective in diverse applications ranging from the estimation of the entropy rate of English texts to the estimation of complexity of chaotic dynamical systems. Additionally, the convergence rate of entropy estimates do not follow from any standard limit theorem, and reported algorithms fail to provide any confidence bounds on the computed values. Exploiting a connection to the theory of probabilistic automata, we establish a convergence rate of O(log|s|/|s|‾‾√3) as a function of the input length |s|, which then yields explicit uncertainty estimates, as well as required data lengths to satisfy pre-specified confidence bounds."]]></description>
<dc:subject>entropy_estimation information_theory statistics stochastic_processes lipson.hod entropy_rate re:AoS_project to_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:15e26f2ca793/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entropy_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lipson.hod"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entropy_rate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1312.6282">
    <title>[1312.6282] Dimension-free Concentration Bounds on Hankel Matrices for Spectral Learning</title>
    <dc:date>2014-01-02T18:41:55+00:00</dc:date>
    <link>http://arxiv.org/abs/1312.6282</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Learning probabilistic models over strings is an important issue for many applications. Spectral methods propose elegant solutions to the problem of inferring weighted automata from finite samples of variable-length strings drawn from an unknown target distribution. These methods rely on a singular value decomposition of a matrix HS, called the Hankel matrix, that records the frequencies of (some of) the observed strings. The accuracy of the learned distribution depends both on the quantity of information embedded in HS and on the distance between HS and its mean Hr. Existing concentration bounds seem to indicate that the concentration over Hr gets looser with the size of Hr, suggesting to make a trade-off between the quantity of used information and the size of Hr. We propose new dimension-free concentration bounds for several variants of Hankel matrices. Experiments demonstrate that these bounds are tight and that they significantly improve existing bounds. These results suggest that the concentration rate of the Hankel matrix around its mean does not constitute an argument for limiting its size."]]></description>
<dc:subject>spectral_methods learning_theory deviation_inequalities markov_models re:AoS_project to_read entableted in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:06bae082a035/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spectral_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:deviation_inequalities"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entableted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://link.springer.com/article/10.1007%2Fs10994-013-5409-9">
    <title>PAutomaC: a probabilistic automata and hidden Markov models learning competition - Online First - Springer</title>
    <dc:date>2013-11-22T17:40:32+00:00</dc:date>
    <link>http://link.springer.com/article/10.1007%2Fs10994-013-5409-9</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Approximating distributions over strings is a hard learning problem. Typical techniques involve using finite state machines as models and attempting to learn these; these machines can either be hand built and then have their weights estimated, or built by grammatical inference techniques: the structure and the weights are then learned simultaneously. The Probabilistic Automata learning Competition (PAutomaC), run in 2012, was the first grammatical inference challenge that allowed the comparison between these methods and algorithms. Its main goal was to provide an overview of the state-of-the-art techniques for this hard learning problem. Both artificial data and real data were presented and contestants were to try to estimate the probabilities of strings. The purpose of this paper is to describe some of the technical and intrinsic challenges such a competition has to face, to give a broad state of the art concerning both the problems dealing with learning grammars and finite state machines and the relevant literature. This paper also provides the results of the competition and a brief description and analysis of the different approaches the main participants used."]]></description>
<dc:subject>to:NB markov_models automata_theory grammar_induction statistics machine_learning to_read re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3f84d97d4918/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:grammar_induction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.sciencedirect.com/science/article/pii/S0167865512003820">
    <title>Picking up the pieces: Causal states in noisy data, and how to recover them</title>
    <dc:date>2013-11-18T21:54:07+00:00</dc:date>
    <link>http://www.sciencedirect.com/science/article/pii/S0167865512003820</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Automatic structure discovery is desirable in many Markov model applications where a good topology (states and transitions) is not known a priori. CSSR is an established pattern discovery algorithm for stationary and ergodic stochastic symbol sequences that learns a predictively optimal Markov representation consisting of so-called causal states. By means of a novel algebraic criterion, we prove that the causal states of a simple process disturbed by random errors frequently are too complex to be learned fully, making CSSR diverge. In fact, the causal state representation of many hidden Markov models, representing simple but noise-disturbed data, has infinite cardinality. We also report that these problems can be solved by endowing CSSR with the ability to make approximations. The resulting algorithm, robust causal states (RCS), is able to recover the underlying causal structure from data corrupted by random substitutions, as is demonstrated both theoretically and in an experiment. The algorithm has potential applications in areas such as error correction and learning stochastic grammars."

- Huh.]]></description>
<dc:subject>to:NB to_read markov_models grammar_induction re:AoS_project entableted</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6f3de3926d00/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:grammar_induction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entableted"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://onlinelibrary.wiley.com/doi/10.1111/sjos.12053/abstract;jsessionid=FB1D1DAFFE181BED5EBB2936B8C7A1E7.f02t02">
    <title>Sparse Markov Chains for Sequence Data - Jääskinen - 2013 - Scandinavian Journal of Statistics - Wiley Online Library</title>
    <dc:date>2013-11-18T14:34:07+00:00</dc:date>
    <link>http://onlinelibrary.wiley.com/doi/10.1111/sjos.12053/abstract;jsessionid=FB1D1DAFFE181BED5EBB2936B8C7A1E7.f02t02</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Finite memory sources and variable-length Markov chains have recently gained popularity in data compression and mining, in particular, for applications in bioinformatics and language modelling. Here, we consider denser data compression and prediction with a family of sparse Bayesian predictive models for Markov chains in finite state spaces. Our approach lumps transition probabilities into classes composed of invariant probabilities, such that the resulting models need not have a hierarchical structure as in context tree-based approaches. This can lead to a substantially higher rate of data compression, and such non-hierarchical sparse models can be motivated for instance by data dependence structures existing in the bioinformatics context. We describe a Bayesian inference algorithm for learning sparse Markov models through clustering of transition probabilities. Experiments with DNA sequence and protein data show that our approach is competitive in both prediction and classification when compared with several alternative methods on the basis of variable memory length."]]></description>
<dc:subject>to:NB markov_models statistical_inference_for_stochastic_processes statistics time_series re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:77e5d7b0fa4c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1309.6819">
    <title>[1309.6819] Hilbert Space Embeddings of Predictive State Representations</title>
    <dc:date>2013-09-27T16:25:27+00:00</dc:date>
    <link>http://arxiv.org/abs/1309.6819</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Predictive State Representations (PSRs) are an expressive class of models for controlled stochastic processes. PSRs represent state as a set of predictions of future observable events. Because PSRs are defined entirely in terms of observable data, statistically consistent estimates of PSR parameters can be learned efficiently by manipulating moments of observed training data. Most learning algorithms for PSRs have assumed that actions and observations are finite with low cardinality. In this paper, we generalize PSRs to infinite sets of observations and actions, using the recent concept of Hilbert space embeddings of distributions. The essence is to represent the state as a nonparametric conditional embedding operator in a Reproducing Kernel Hilbert Space (RKHS) and leverage recent work in kernel methods to estimate, predict, and update the representation. We show that these Hilbert space embeddings of PSRs are able to gracefully handle continuous actions and observations, and that our learned models outperform competing system identification algorithms on several prediction benchmarks."]]></description>
<dc:subject>to:NB markov_models time_series machine_learning hilbert_space stochastic_processes gordon.geoffrey to_read re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:30991b3ae3c8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:gordon.geoffrey"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6532389">
    <title>IEEE Xplore - Universal Tests for Memory Words</title>
    <dc:date>2013-09-17T20:33:28+00:00</dc:date>
    <link>http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6532389</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The main result is a universal pointwise test that, when presented with a set of words $S$ on a finite or countable alphabet ${cal X}$ that purports to be a set of memory words for a stationary process, will eventually almost surely return the value YES precisely when all positive probability words in $S$ are memory words. For example, if $S$ consists of all of the single letters in ${cal X}$, then the test will eventually say yes if and only if the process is a Markov chain. Various further positive and negative results of this type are also given."]]></description>
<dc:subject>to:NB stochastic_processes automata_theory markov_models re:AoS_project to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:741708b10395/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1309.3792">
    <title>[1309.3792] Exact Complexity: The Spectral Decomposition of Intrinsic Computation</title>
    <dc:date>2013-09-17T20:32:04+00:00</dc:date>
    <link>http://arxiv.org/abs/1309.3792</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full eigenvalue spectrum of the mixed-state presentation of a process's epsilon-machine causal-state dynamic. Measures include correlation functions, power spectra, past-future mutual information, transient and synchronization informations, and many others. As a result, a direct and complete analysis of intrinsic computation is now available for the temporal organization of finitary hidden Markov models and nonlinear dynamical systems with generating partitions and for the spatial organization in one-dimensional systems, including spin systems, cellular automata, and complex materials via chaotic crystallography."]]></description>
<dc:subject>to:NB spectral_methods complexity_measures information_theory markov_models kith_and_kin crutchfield.james_p. stochastic_processes re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:834717f3080a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spectral_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:complexity_measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:crutchfield.james_p."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1309.2819">
    <title>[1309.2819] Stochastic processes with random contexts: a characterization, and adaptive estimators for the transition probabilities</title>
    <dc:date>2013-09-12T20:04:48+00:00</dc:date>
    <link>http://arxiv.org/abs/1309.2819</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper introduces the concept of random context representations for the transition probabilities of a finite-alphabet stochastic process. Processes with these representations generalize context tree processes (a.k.a. variable length Markov chains), and are proven to coincide with processes whose transition probabilities are almost surely continuous functions of the (infinite) past. This is similar to a classical result by Kalikow about continuous transition probabilities. Existence and uniqueness of a minimal random context representation are proven, and an estimator of the transition probabilities based on this representation is shown to have very good "pastwise adaptativity" properties. In particular, it achieves minimax performance, up to logarithmic factors, for binary renewal processes with bounded $2+\gamma$ moments."]]></description>
<dc:subject>stochastic_processes symbolic_dynamics markov_models re:AoS_project to_read in_NB variable-length_markov_models_aka_context_trees</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a98a1bc5fa66/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:symbolic_dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variable-length_markov_models_aka_context_trees"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1011.1581">
    <title>[1011.1581] Asymptotic Synchronization for Finite-State Sources</title>
    <dc:date>2013-09-06T11:39:19+00:00</dc:date>
    <link>http://arxiv.org/abs/1011.1581</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We extend a recent synchronization analysis of exact finite-state sources to nonexact sources for which synchronization occurs only asymptotically. Although the proof methods are quite different, the primary results remain the same. We find that an observer's average uncertainty in the source state vanishes exponentially fast and, as a consequence, an observer's average uncertainty in predicting future output converges exponentially fast to the source entropy rate."]]></description>
<dc:subject>to:NB stochastic_processes to_read markov_models automata_theory information_theory re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a2f002e17a40/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://papers.nips.cc/paper/4697-spectral-learning-of-general-weighted-automata-via-constrained-matrix-completion">
    <title>Spectral Learning of General Weighted Automata via Constrained Matrix Completion</title>
    <dc:date>2013-05-07T22:03:41+00:00</dc:date>
    <link>http://papers.nips.cc/paper/4697-spectral-learning-of-general-weighted-automata-via-constrained-matrix-completion</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Many tasks in text and speech processing and computational biology require es- timating functions mapping strings to real numbers. A broad class of such func- tions can be defined by weighted automata. Spectral methods based on the sin- gular value decomposition of a Hankel matrix have been recently proposed for learning a probability distribution represented by a weighted automaton from a training sample drawn according to this same target distribution. In this paper, we show how spectral methods can be extended to the problem of learning a general weighted automaton from a sample generated by an arbitrary distribution. The main obstruction to this approach is that, in general, some entries of the Hankel matrix may be missing. We present a solution to this problem based on solving a constrained matrix completion problem. Combining these two ingredients, matrix completion and spectral method, a whole new family of algorithms for learning general weighted automata is obtained. We present generalization bounds for a particular algorithm in this family. The proofs rely on a joint stability analysis of matrix completion and spectral learning."]]></description>
<dc:subject>to:NB to_read low-rank_approximation spectral_methods automata_theory mohri.mehryar re:AoS_project machine_learning grammar_induction entableted</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f478f1bfe393/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:low-rank_approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spectral_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mohri.mehryar"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:grammar_induction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entableted"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1304.6603">
    <title>[1304.6603] Optimal Kullback-Leibler Aggregation via Information Bottleneck</title>
    <dc:date>2013-04-25T16:42:40+00:00</dc:date>
    <link>http://arxiv.org/abs/1304.6603</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper presents a method for reduction of Markov models with large state spaces based on information-theoretic criteria. As a cost function we define the Kullback-Leibler divergence rate between the process obtained by simply partitioning the alphabet of the original chain (which in general is not Markov) and its best Markov approximation. We further show that the Kullback-Leibler divergence rate between the original chain and the lifting of the optimal Markov approximation yields an easy-to-compute upper bound on the cost function. 
"By properly defining the lifting, the present work obtains a reduction which is closely related to the notion of lumpability. It is further shown that the cost function can be minimized by employing the information bottleneck method, thus building a bridge between Markov theory, control systems, and machine learning."]]></description>
<dc:subject>to:NB information_theory macro_from_micro markov_models stochastic_processes information_bottleneck re:AoS_project to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5c22017d9090/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:macro_from_micro"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_bottleneck"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1304.4806">
    <title>[1304.4806] Unsupervised model-free representation learning</title>
    <dc:date>2013-04-22T17:54:20+00:00</dc:date>
    <link>http://arxiv.org/abs/1304.4806</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Numerous control and learning problems face the situation where sequences of high-dimensional highly dependent data are available, but no or little feedback is provided to the learner. To address this issue, we formulate the following problem. Given a series of observations X_0,...,X_n coming from a large (high-dimensional) space X, find a representation function f mapping X to a finite space Y such that the series f(X_0),...,f(X_n) preserve as much information as possible about the original time-series dependence in X_0,...,X_n. We show that, for stationary time series, the function f can be selected as the one maximizing the time-series information h_0(f(X))- h_\infty (f(X)) where h_0(f(X)) is the Shannon entropy of f(X_0) and h_\infty (f(X)) is the entropy rate of the time series f(X_0),...,f(X_n),... Implications for the problem of optimal control are presented."]]></description>
<dc:subject>to:NB information_theory stochastic_processes re:AoS_project ryabko.daniil to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:25091859a6c2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ryabko.daniil"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/math/0508607">
    <title>[math/0508607] Approximating a sequence of observations by a simple process</title>
    <dc:date>2013-04-13T22:11:54+00:00</dc:date>
    <link>http://arxiv.org/abs/math/0508607</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step transitions along a realization from the approximating process, are close to that of the given sequence. We generalize the result to the case where the one-step transitions are required to be in given polyhedra."]]></description>
<dc:subject>to:NB prediction markov_models statistics re:AoS_project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9ff7ce475deb/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/cs/0508127">
    <title>[cs/0508127] On context-tree prediction of individual sequences</title>
    <dc:date>2013-04-13T22:10:47+00:00</dc:date>
    <link>http://arxiv.org/abs/cs/0508127</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Motivated by the evident success of context-tree based methods in lossless data compression, we explore, in this paper, methods of the same spirit in universal prediction of individual sequences. By context-tree prediction, we refer to a family of prediction schemes, where at each time instant $t$, after having observed all outcomes of the data sequence $x_1,...,x_{t-1}$, but not yet $x_t$, the prediction is based on a ``context'' (or a state) that consists of the $k$ most recent past outcomes $x_{t-k},...,x_{t-1}$, where the choice of $k$ may depend on the contents of a possibly longer, though limited, portion of the observed past, $x_{t-k_{\max}},...x_{t-1}$. This is different from the study reported in [1], where general finite-state predictors as well as ``Markov'' (finite-memory) predictors of fixed order, were studied in the regime of individual sequences. 
"Another important difference between this study and [1] is the asymptotic regime. While in [1], the resources of the predictor (i.e., the number of states or the memory size) were kept fixed regardless of the length $N$ of the data sequence, here we investigate situations where the number of contexts or states is allowed to grow concurrently with $N$. We are primarily interested in the following fundamental question: What is the critical growth rate of the number of contexts, below which the performance of the best context-tree predictor is still universally achievable, but above which it is not? We show that this critical growth rate is linear in $N$. In particular, we propose a universal context-tree algorithm that essentially achieves optimum performance as long as the growth rate is sublinear, and show that, on the other hand, this is impossible in the linear case."]]></description>
<dc:subject>to:NB information_theory prediction individual_sequence_prediction markov_models re:AoS_project variable-length_markov_models_aka_context_trees</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:54fe82cb3afa/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:individual_sequence_prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variable-length_markov_models_aka_context_trees"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1208.3728">
    <title>[1208.3728] Online Learning with Predictable Sequences</title>
    <dc:date>2012-08-24T11:27:03+00:00</dc:date>
    <link>http://arxiv.org/abs/1208.3728</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present methods for online linear optimization that take advantage of benign (as opposed to worst-case) sequences. Specifically if the sequence encountered by the learner is described well by a known "predictable process", the algorithms presented enjoy tighter bounds as compared to the typical worst case bounds. Additionally, the methods achieve the usual worst-case regret bounds if the sequence is not benign. Our approach can be seen as a way of adding prior knowledge about the sequence within the paradigm of online learning. The setting is shown to encompass partial and side information. Variance and path-length bounds can be seen as particular examples of online learning with simple predictable sequences. 
"We further extend our methods and results to include competing with a set of possible predictable processes (models), that is "learning" the predictable process itself concurrently with using it to obtain better regret guarantees. We show that such model selection is possible under various assumptions on the available feedback. Our results suggest a promising direction of further research with potential applications to stock market and time series prediction."]]></description>
<dc:subject>online_learning learning_theory machine_learning time_series re:AoS_project rakhlin.alexander low-regret_learning in_NB heard_the_talk</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f9c66b95f97b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:online_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:rakhlin.alexander"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:low-regret_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:heard_the_talk"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1207.4678">
    <title>[1207.4678] Uniform Chernoff and Dvoretzky-Kiefer-Wolfowitz-type inequalities for Markov chains and related processes</title>
    <dc:date>2012-07-21T16:25:44+00:00</dc:date>
    <link>http://arxiv.org/abs/1207.4678</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We observe that the technique of Markov contraction can be used to establish measure concentration for a broad class of non-contracting chains. In particular, geometric ergodicity provides a simple and versatile framework. This leads to a short, elementary proof of a general concentration inequality for Markov and hidden Markov chains (HMM), which supercedes some of the known results and easily extends to other processes such as Markov trees. As applications, we give a Dvoretzky-Kiefer-Wolfowitz-type inequality and a uniform Chernoff bound. All of our bounds are dimension-free and hold for countably infinite state spaces."]]></description>
<dc:subject>stochastic_processes markov_models kontorovich.aryeh kith_and_kin re:AoS_project in_NB have_read deviation_inequalities</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:01a366c4908a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kontorovich.aryeh"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:deviation_inequalities"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1207.1238">
    <title>[1207.1238] On the Hardness of Entropy Minimization and Related Problems</title>
    <dc:date>2012-07-09T18:56:58+00:00</dc:date>
    <link>http://arxiv.org/abs/1207.1238</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We investigate certain optimization problems for Shannon information measures, namely, minimization of joint and conditional entropies $H(X,Y)$, $H(X|Y)$, $H(Y|X)$, and maximization of mutual information $I(X;Y)$, over convex regions. When restricted to the so-called transportation polytopes (sets of distributions with fixed marginals), very simple proofs of NP-hardness are obtained for these problems because in that case they are all equivalent, and their connection to the well-known textsc{Subset sum} and textsc{Partition} problems is revealed. The computational intractability of the more general problems over arbitrary polytopes is then a simple consequence. Further, a simple class of polytopes is shown over which the above problems are not equivalent and their complexity differs sharply, namely, minimization of $H(X,Y)$ and $H(Y|X)$ is trivial, while minimization of $H(X|Y)$ and maximization of $I(X;Y)$ are strongly NP-hard problems. Finally, two new (pseudo)metrics on the space of discrete probability distributions are introduced, based on the so-called variation of information quantity, and NP-hardness of their computation is shown."]]></description>
<dc:subject>to:NB to_read information_theory re:AoS_project optimization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3fa7f206a82e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
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