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  </channel><item rdf:about="https://www.stat.umn.edu/geyer/8931expfam/newnew.pdf">
    <title>Exponential Families on Abstract Affine Spaces (Geyer, 2024)</title>
    <dc:date>2024-04-29T17:35:50+00:00</dc:date>
    <link>https://www.stat.umn.edu/geyer/8931expfam/newnew.pdf</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>to:NB exponential_families geyer.charles_j. mathematics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6baaf2bae286/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/2111.14152">
    <title>[2111.14152] An inverse Sanov theorem for exponential families</title>
    <dc:date>2022-06-19T17:06:01+00:00</dc:date>
    <link>https://arxiv.org/abs/2111.14152</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We prove the large deviation principle (LDP) for posterior distributions arising from subfamilies of full exponential families, allowing misspecification of the model. Moreover, motivated by the so-called inverse Sanov Theorem (see e.g. Ganesh and O'Connell 1999 and 2000), we prove the LDP for the corresponding maximum likelihood estimator, and we study the relationship between rate functions. In our setting, even in the non misspecified case, it is not true in general that the rate functions for posterior distributions and for maximum likelihood estimators are Kullback-Leibler divergences with exchanged arguments."]]></description>
<dc:subject>bayesian_consistency statistics large_deviations to_read re:bayes_as_evol exponential_families in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:cc076a9e954b/</dc:identifier>
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<item rdf:about="https://projecteuclid.org/journals/annals-of-statistics/volume-49/issue-3/Total-positivity-in-exponential-families-with-application-to-binary-variables/10.1214/20-AOS2007.short">
    <title>Total positivity in exponential families with application to binary variables</title>
    <dc:date>2021-08-10T14:09:30+00:00</dc:date>
    <link>https://projecteuclid.org/journals/annals-of-statistics/volume-49/issue-3/Total-positivity-in-exponential-families-with-application-to-binary-variables/10.1214/20-AOS2007.short</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study exponential families of distributions that are multivariate totally positive of order 2 (MTP2), show that these are convex exponential families and derive conditions for existence of the MLE. Quadratic exponential familes of MTP2 distributions contain attractive Gaussian graphical models and ferromagnetic Ising models as special examples. We show that these are defined by intersecting the space of canonical parameters with a polyhedral cone whose faces correspond to conditional independence relations. Hence MTP2 serves as an implicit regularizer for quadratic exponential families and leads to sparsity in the estimated graphical model. We prove that the maximum likelihood estimator (MLE) in an MTP2 binary exponential family exists if and only if both of the sign patterns (1,−1) and (−1,1) are represented in the sample for every pair of variables; in particular, this implies that the MLE may exist with n=d observations, in stark contrast to unrestricted binary exponential families where 2^d observations are required. Finally, we provide a novel and globally convergent algorithm for computing the MLE for MTP2 Ising models similar to iterative proportional scaling and apply it to the analysis of data from two psychological disorders."]]></description>
<dc:subject>to_read exponential_families graphical_models uhler.caroline lauritzen.steffen of_course_its_really_a_spin_glass in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c1464c953dee/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/2106.10496">
    <title>[2106.10496] The Tangent Exponential Model</title>
    <dc:date>2021-06-24T21:12:06+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.10496</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The likelihood function is central to both frequentist and Bayesian formulations of parametric statistical inference, and large-sample approximations to the sampling distributions of estimators and test statistics, and to posterior densities, are widely used in practice. Improved approximations have been widely studied and can provide highly accurate inferences when samples are small or there are many nuisance parameters. This article reviews improved approximations based on the tangent exponential model developed in a series of articles by D.~A.~S.~Fraser and co-workers, attempting to explain the theoretical basis of this model and to provide a guide to the associated literature, including a partially-annotated bibliography."]]></description>
<dc:subject>to:NB likelihood exponential_families statistics re:HEAS</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ed7c6b92148c/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/2105.05106">
    <title>[2105.05106] A General Derivative Identity for the Conditional Expectation with Focus on the Exponential Family</title>
    <dc:date>2021-05-12T18:19:13+00:00</dc:date>
    <link>https://arxiv.org/abs/2105.05106</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Consider a pair of random vectors (X,Y) and the conditional expectation operator 𝔼[X|Y=y]. This work studies analytic properties of the conditional expectation by characterizing various derivative identities. The paper consists of two parts. In the first part of the paper, a general derivative identity for the conditional expectation is derived. Specifically, for the Markov chain U↔X↔Y, a compact expression for the Jacobian matrix of 𝔼[U|Y=y] is derived. In the second part of the paper, the main identity is specialized to the exponential family. Moreover, via various choices of the random vector U, the new identity is used to recover and generalize several known identities and derive some new ones. As a first example, a connection between the Jacobian of 𝔼[X|Y=y] and the conditional variance is established. As a second example, a recursive expression between higher order conditional expectations is found, which is shown to lead to a generalization of the Tweedy's identity. Finally, as a third example, it is shown that the k-th order derivative of the conditional expectation is proportional to the (k+1)-th order conditional cumulant."

--- Application to instrumental variables?]]></description>
<dc:subject>to:NB probability to_read exponential_families</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:271b96239ee0/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/2012.15480">
    <title>[2012.15480] Likelihood Ratio Exponential Families</title>
    <dc:date>2021-01-19T18:50:53+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.15480</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The exponential family is well known in machine learning and statistical physics as the maximum entropy distribution subject to a set of observed constraints, while the geometric mixture path is common in MCMC methods such as annealed importance sampling. Linking these two ideas, recent work has interpreted the geometric mixture path as an exponential family of distributions to analyze the thermodynamic variational objective (TVO).
"We extend these likelihood ratio exponential families to include solutions to rate-distortion (RD) optimization, the information bottleneck (IB) method, and recent rate-distortion-classification approaches which combine RD and IB. This provides a common mathematical framework for understanding these methods via the conjugate duality of exponential families and hypothesis testing. Further, we collect existing results to provide a variational representation of intermediate RD or TVO distributions as a minimizing an expectation of KL divergences. This solution also corresponds to a size-power tradeoff using the likelihood ratio test and the Neyman Pearson lemma. In thermodynamic integration bounds such as the TVO, we identify the intermediate distribution whose expected sufficient statistics match the log partition function."]]></description>
<dc:subject>to:NB exponential_families likelihood information_theory information_geometry galstyan.aram ver_steeg.greg to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:790cf9c3e391/</dc:identifier>
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<item rdf:about="https://www.cambridge.org/core/journals/proceedings-of-the-international-astronomical-union/article/potential-of-likelihoodfree-inference-of-cosmological-parameters-with-weak-lensing-data/0E1FEF317A0C09039B52C8791E63670D">
    <title>The potential of likelihood-free inference of cosmological parameters with weak lensing data | Proceedings of the International Astronomical Union | Cambridge Core</title>
    <dc:date>2020-12-13T23:58:29+00:00</dc:date>
    <link>https://www.cambridge.org/core/journals/proceedings-of-the-international-astronomical-union/article/potential-of-likelihoodfree-inference-of-cosmological-parameters-with-weak-lensing-data/0E1FEF317A0C09039B52C8791E63670D</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In the statistical framework of likelihood-free inference, the posterior distribution of model parameters is explored via simulation rather than direct evaluation of the likelihood function, permitting inference in situations where this function is analytically intractable. We consider the problem of estimating cosmological parameters using measurements of the weak gravitational lensing of galaxies; specifically, we propose the use a likelihood-free approach to investigate the posterior distribution of some parameters in the ΛCDM model upon observing a large number of sheared galaxies. The choice of summary statistic used when comparing observed data and simulated data in the likelihood-free inference framework is critical, so we work toward a principled method of choosing the summary statistic, aiming for dimension reduction while seeking a statistic that is as close as possible to being sufficient for the parameters of interest."]]></description>
<dc:subject>have_read heard_the_talk approved_the_thesis astronomy approximate_bayesian_computation sufficiency exponential_families dimension_reduction simulation-based_estimation statistics in_NB re:codename:catherine_wheel</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:af0f8495eafc/</dc:identifier>
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<item rdf:about="https://www.cambridge.org/9781108701112">
    <title>Statistical modelling with exponential families | Statistical theory and methods | Cambridge University Press</title>
    <dc:date>2020-01-09T17:46:09+00:00</dc:date>
    <link>https://www.cambridge.org/9781108701112</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Löf in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exercises embedded within the text as well as at the ends of chapters."]]></description>
<dc:subject>in_NB exponential_families statistics books:noted books:suggest_to_library</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b8b44d223ee7/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/1910.13398">
    <title>[1910.13398] Stein's Lemma for the Reparameterization Trick with Exponential Family Mixtures</title>
    <dc:date>2019-10-30T13:34:12+00:00</dc:date>
    <link>https://arxiv.org/abs/1910.13398</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Stein's method (Stein, 1973; 1981) is a powerful tool for statistical applications, and has had a significant impact in machine learning. Stein's lemma plays an essential role in Stein's method. Previous applications of Stein's lemma either required strong technical assumptions or were limited to Gaussian distributions with restricted covariance structures. In this work, we extend Stein's lemma to exponential-family mixture distributions including Gaussian distributions with full covariance structures. Our generalization enables us to establish a connection between Stein's lemma and the reparamterization trick to derive gradients of expectations of a large class of functions under weak assumptions. Using this connection, we can derive many new reparameterizable gradient-identities that goes beyond the reach of existing works. For example, we give gradient identities when expectation is taken with respect to Student's t-distribution, skew Gaussian, exponentially modified Gaussian, and normal inverse Gaussian."]]></description>
<dc:subject>to:NB probability exponential_families</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:31bd83997d38/</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:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1811.01394">
    <title>[1811.01394] A method to construct exponential families by representation theory</title>
    <dc:date>2019-08-20T14:52:48+00:00</dc:date>
    <link>https://arxiv.org/abs/1811.01394</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we give a method to construct "good" exponential families systematically by representation theory. More precisely, we consider a homogeneous space G/H as a sample space and construct an exponential family invariant under the transformation group G by using a representation of G. The method generates widely used exponential families such as normal, gamma, Bernoulli, categorical, Wishart, von Mises, Fisher-Bingham and hyperboloid distributions."]]></description>
<dc:subject>to:NB exponential_families algebra statistics probability</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a09d7a1b1a6b/</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:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:algebra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.cambridge.org/us/academic/subjects/statistics-probability/statistical-theory-and-methods/statistical-modelling-exponential-families?format=PB&amp;WT.mc_id=LFA-STA-CL-ComingSoon%2B-April-2019">
    <title>Statistical modelling with exponential families</title>
    <dc:date>2019-05-14T23:35:03+00:00</dc:date>
    <link>https://www.cambridge.org/us/academic/subjects/statistics-probability/statistical-theory-and-methods/statistical-modelling-exponential-families?format=PB&amp;WT.mc_id=LFA-STA-CL-ComingSoon%2B-April-2019</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Löf in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exercises embedded within the text as well as at the ends of chapters."]]></description>
<dc:subject>books:noted exponential_families exponential_family_random_graphs statistical_mechanics statistics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:71929c6f2d1c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_family_random_graphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.jmlr.org/papers/v18/16-011.html">
    <title>Density Estimation in Infinite Dimensional Exponential Families</title>
    <dc:date>2018-07-23T16:10:55+00:00</dc:date>
    <link>http://www.jmlr.org/papers/v18/16-011.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we consider an infinite dimensional exponential family P of probability densities, which are parametrized by functions in a reproducing kernel Hilbert space H, and show it to be quite rich in the sense that a broad class of densities on ℝdRd can be approximated arbitrarily well in Kullback-Leibler (KL) divergence by elements in P. Motivated by this approximation property, the paper addresses the question of estimating an unknown density p0p0 through an element in P. Standard techniques like maximum likelihood estimation (MLE) or pseudo MLE (based on the method of sieves), which are based on minimizing the KL divergence between p0p0 and P, do not yield practically useful estimators because of their inability to efficiently handle the log-partition function. We propose an estimator p̂ np^n based on minimizing the Fisher divergence, J(p0‖p)J(p0‖p) between p0p0 and p∈p∈P, which involves solving a simple finite-dimensional linear system. When p0∈p0∈P, we show that the proposed estimator is consistent, and provide a convergence rate of n−min{23,2β+12β+2}n−min{23,2β+12β+2} in Fisher divergence under the smoothness assumption that logp0∈(Cβ)log⁡p0∈R(Cβ) for some β≥0β≥0, where CC is a certain Hilbert-Schmidt operator on H and (Cβ)R(Cβ) denotes the image of CβCβ. We also investigate the misspecified case of p0∉p0∉P and show that J(p0‖p̂ n)→infp∈J(p0‖p)J(p0‖p^n)→infp∈PJ(p0‖p) as n→∞n→∞, and provide a rate for this convergence under a similar smoothness condition as above. Through numerical simulations we demonstrate that the proposed estimator outperforms the non- parametric kernel density estimator, and that the advantage of the proposed estimator grows as dd increases."]]></description>
<dc:subject>density_estimation exponential_families statistics via:? in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:96131f032145/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<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="https://arxiv.org/abs/1406.0423">
    <title>[1406.0423] Targeted Maximum Likelihood Estimation using Exponential Families</title>
    <dc:date>2017-10-04T17:35:18+00:00</dc:date>
    <link>https://arxiv.org/abs/1406.0423</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We investigate the use of exponential families to define the parametric submodel. This implementation of TMLE gives a general approach for estimating any smooth parameter in the nonparametric model. A computational advantage of this approach is that each iteration of TMLE involves estimation of a parameter in an exponential family, which is a convex optimization problem for which software implementing reliable and computationally efficient methods exists. We illustrate the method in three estimation problems, involving the mean of an outcome missing at random, the parameter of a median regression model, and the causal effect of a continuous exposure, respectively. We conduct a simulation study comparing different choices for the parametric submodel, focusing on the first of these problems. To the best of our knowledge, this is the first study investigating robustness of TMLE to different specifications of the parametric submodel. We find that the choice of submodel can have an important impact on the behavior of the estimator in finite samples."]]></description>
<dc:subject>to:NB statistics estimation nonparametrics causal_inference exponential_families</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:216e754c640e/</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:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1210.6516">
    <title>[1210.6516] The RKHS Approach to Minimum Variance Estimation Revisited: Variance Bounds, Sufficient Statistics, and Exponential Families</title>
    <dc:date>2016-12-01T20:22:46+00:00</dc:date>
    <link>https://arxiv.org/abs/1210.6516</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The mathematical theory of reproducing kernel Hilbert spaces (RKHS) provides powerful tools for minimum variance estimation (MVE) problems. Here, we extend the classical RKHS based analysis of MVE in several directions. We develop a geometric formulation of five known lower bounds on the estimator variance (Barankin bound, Cramer-Rao bound, constrained Cramer-Rao bound, Bhattacharyya bound, and Hammersley-Chapman-Robbins bound) in terms of orthogonal projections onto a subspace of the RKHS associated with a given MVE problem. We show that, under mild conditions, the Barankin bound (the tightest possible lower bound on the estimator variance) is a lower semicontinuous function of the parameter vector. We also show that the RKHS associated with an MVE problem remains unchanged if the observation is replaced by a sufficient statistic. Finally, for MVE problems conforming to an exponential family of distributions, we derive novel closed-form lower bound on the estimator variance and show that a reduction of the parameter set leaves the minimum achievable variance unchanged."]]></description>
<dc:subject>hilbert_space estimation statistics sufficiency exponential_families in_NB cramer-rao_inequality</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:83ff304feed7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sufficiency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cramer-rao_inequality"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.aos/1009210550">
    <title>Geiger , Heckerman , King , Meek : Stratified exponential families: Graphical models and model selection</title>
    <dc:date>2016-07-08T15:18:25+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.aos/1009210550</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We describe a hierarchy of exponential families which is useful for distinguishing types of graphical models. Undirected graphical models with no hidden variables are linear exponential families (LEFs). Directed acyclic graphical (DAG) models and chain graphs with no hidden variables, includ­ ing DAG models with several families of local distributions, are curved exponential families (CEFs). Graphical models with hidden variables are what we term stratified exponential families (SEFs). A SEF is a finite union of CEFs of various dimensions satisfying some regularity conditions. We also show that this hierarchy of exponential families is noncollapsing with respect to graphical models by providing a graphical model which is a CEF but not a LEF and a graphical model that is a SEF but not a CEF. Finally, we show how to compute the dimension of a stratified exponential family. These results are discussed in the context of model selection of graphical models."]]></description>
<dc:subject>to:NB have_read graphical_models exponential_families statistics geometry via:rvenkat</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4a247e15daf6/</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:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:rvenkat"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://auai.org/uai2015/proceedings/papers/120.pdf">
    <title>Estimating the Partition Function by Discriminance Sampling</title>
    <dc:date>2015-07-15T13:51:00+00:00</dc:date>
    <link>http://auai.org/uai2015/proceedings/papers/120.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Importance sampling (IS) and its variant, an- nealed IS (AIS) have been widely used for es- timating the partition function in graphical mod- els, such as Markov random fields and deep gen- erative models. However, IS tends to underesti- mate the partition function and is subject to high variance when the proposal distribution is more peaked than the target distribution. On the other hand, “reverse” versions of IS and AIS tend to overestimate the partition function, and degener- ate when the target distribution is more peaked than the proposal distribution. In this work, we present a simple, general method that gives much more reliable and robust estimates than either IS (AIS) or reverse IS (AIS). Our method works by converting the estimation problem into a simple classification problem that discriminates between the samples drawn from the target and the pro- posal. We give extensive theoretical and empir- ical justification; in particular, we show that an annealed version of our method significantly out- performs both AIS and reverse AIS as proposed by Burda et al. (2015), which has been the state- of-the-art for likelihood evaluation in deep gen- erative models."]]></description>
<dc:subject>heard_the_talk computational_statistics exponential_families statistics monte_carlo classifiers in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a99f09e5c6f8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:heard_the_talk"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:monte_carlo"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:classifiers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.aos/1407420005">
    <title>Evans , Richardson : Markovian acyclic directed mixed graphs for discrete data</title>
    <dc:date>2015-02-23T07:23:06+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.aos/1407420005</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Acyclic directed mixed graphs (ADMGs) are graphs that contain directed (→) and bidirected (↔) edges, subject to the constraint that there are no cycles of directed edges. Such graphs may be used to represent the conditional independence structure induced by a DAG model containing hidden variables on its observed margin. The Markovian model associated with an ADMG is simply the set of distributions obeying the global Markov property, given via a simple path criterion (m-separation). We first present a factorization criterion characterizing the Markovian model that generalizes the well-known recursive factorization for DAGs. For the case of finite discrete random variables, we also provide a parameterization of the model in terms of simple conditional probabilities, and characterize its variation dependence. We show that the induced models are smooth. Consequently, Markovian ADMG models for discrete variables are curved exponential families of distributions."]]></description>
<dc:subject>graphical_models probability richardson.thomas exponential_families in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0a97151e6bcb/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:richardson.thomas"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<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/yang14a.html">
    <title>Mixed Graphical Models via Exponential Families | AISTATS 2014 | JMLR W&amp;CP</title>
    <dc:date>2014-04-15T12:34:15+00:00</dc:date>
    <link>http://jmlr.org/proceedings/papers/v33/yang14a.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Markov Random Fields, or undirected graphical models are widely used to model high-dimensional multivariate data. Classical instances of these models, such as Gaussian Graphical and Ising Models, as well as recent extensions to graphical models specified by univariate exponential families, assume all variables arise from the same distribution. Complex data from high-throughput genomics and social networking for example, often contain discrete, count, and continuous variables measured on the same set of samples. To model such heterogeneous data, we develop a novel class of mixed graphical models by specifying that each node-conditional distribution is a member of a possibly different univariate exponential family. We study several instances of our model, and propose scalable M-estimators for recovering the underlying network structure. Simulations as well as an application to learning mixed genomic networks from next generation sequencing and mutation data demonstrate the versatility of our methods."

--- Um.  Haven't people been doing this in practice since about forever?]]></description>
<dc:subject>to:NB graphical_models exponential_families statistics ravikumar.pradeep allen.genevera_i. color_me_skeptical</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a7f1acf01551/</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:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ravikumar.pradeep"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:allen.genevera_i."/>
	<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/1401.3814">
    <title>[1401.3814] Information Geometry Approach to Parameter Estimation in Markov Chains</title>
    <dc:date>2014-03-10T02:16:31+00:00</dc:date>
    <link>http://arxiv.org/abs/1401.3814</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then, we show that the sample mean of the generator of the exponential family is an asymptotically efficient estimator. Further, we also define a curved exponential family of transition matrices. Using a transition matrix version of the Pythagorean theorem, we give an asymptotically efficient estimator for a curved exponential family."

--- The abstract makes this sound like a lot of math to recover what's in Billingsley (1961).  Hopefully there's more to it than this.]]></description>
<dc:subject>to:NB markov_models exponential_families information_geometry statistical_inference_for_stochastic_processes statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b45a741c4372/</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:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_geometry"/>
	<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:Bag></taxo:topics>
</item>
<item rdf:about="http://papers.nips.cc/paper/5154-conditional-random-fields-via-univariate-exponential-families">
    <title>Conditional Random Fields via Univariate Exponential Families</title>
    <dc:date>2014-01-04T03:34:39+00:00</dc:date>
    <link>http://papers.nips.cc/paper/5154-conditional-random-fields-via-univariate-exponential-families</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Conditional random fields, which model the distribution of a multivariate response conditioned on a set of covariates using undirected graphs, are widely used in a variety of multivariate prediction applications. Popular instances of this class of models such as categorical-discrete CRFs, Ising CRFs, and conditional Gaussian based CRFs, are not however best suited to the varied types of response variables in many applications, including count-valued responses. We thus introduce a “novel subclass of CRFs”, derived by imposing node-wise conditional distributions of response variables conditioned on the rest of the responses and the covariates as arising from univariate exponential families. This allows us to derive novel multivariate CRFs given any univariate exponential distribution, including the Poisson, negative binomial, and exponential distributions. Also in particular, it addresses the common CRF problem of specifying feature'' functions determining the interactions between response variables and covariates. We develop a class of tractable penalized M-estimators to learn these CRF distributions from data, as well as a unified sparsistency analysis for this general class of CRFs showing exact structure recovery can be achieved with high probability."]]></description>
<dc:subject>random_fields exponential_families graphical_models statistics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2dedac961c9a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1312.3625">
    <title>[1312.3625] Efficient prediction in $L^2$-differentiable families of distributions</title>
    <dc:date>2013-12-16T01:52:02+00:00</dc:date>
    <link>http://arxiv.org/abs/1312.3625</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A proof of the Cram\'er-Rao inequality for prediction is presented under conditions of L2-differentiability of the family of distributions of the model. The assumptions and the proof differ from those of Miyata (2001) who also proved this inequality under L2-differentiability conditions. It is also proved that an efficient predictor (i.e. which risk attains the bound) exists if and only if the family of distributions is of a special form which can be seen as an extension of the notion of exponential family. This result is also proved under L2-differentiability conditions."]]></description>
<dc:subject>to:NB prediction statistics exponential_families cramer-rao_inequality</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:245f43a4cb9c/</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:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cramer-rao_inequality"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1208.2992">
    <title>[1208.2992] Critical phenomena in exponential random graphs</title>
    <dc:date>2013-09-23T13:16:41+00:00</dc:date>
    <link>http://arxiv.org/abs/1208.2992</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence between particle states in a grand canonical ensemble of statistical physics. By adjusting the specific values of these subgraph densities, one can analyze the influence of various local features on the global structure of the network. Loosely put, a phase transition occurs when a singularity arises in the limiting free energy density, as it is the generating function for the limiting expectations of all thermodynamic observables. We derive the full phase diagram for a large family of 3-parameter exponential random graph models with attraction and show that they all consist of a first order surface phase transition bordered by a second order critical curve."]]></description>
<dc:subject>exponential_families exponential_family_random_graphs phase_transitions statistical_mechanics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:70573f5d6bab/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_family_random_graphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:phase_transitions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1212.2512">
    <title>[1212.2512] A Generalized Mean Field Algorithm for Variational Inference in Exponential Families</title>
    <dc:date>2013-09-10T19:09:29+00:00</dc:date>
    <link>http://arxiv.org/abs/1212.2512</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The mean field methods, which entail approximating intractable probability distributions variationally with distributions from a tractable family, enjoy high efficiency, guaranteed convergence, and provide lower bounds on the true likelihood. But due to requirement for model-specific derivation of the optimization equations and unclear inference quality in various models, it is not widely used as a generic approximate inference algorithm. In this paper, we discuss a generalized mean field theory on variational approximation to a broad class of intractable distributions using a rich set of tractable distributions via constrained optimization over distribution spaces. We present a class of generalized mean field (GMF) algorithms for approximate inference in complex exponential family models, which entails limiting the optimization over the class of cluster-factorizable distributions. GMF is a generic method requiring no model-specific derivations. It factors a complex model into a set of disjoint variable clusters, and uses a set of canonical fix-point equations to iteratively update the cluster distributions, and converge to locally optimal cluster marginals that preserve the original dependency structure within each cluster, hence, fully decomposed the overall inference problem. We empirically analyzed the effect of different tractable family (clusters of different granularity) on inference quality, and compared GMF with BP on several canonical models. Possible extension to higher-order MF approximation is also discussed."]]></description>
<dc:subject>have_read graphical_models exponential_families statistics variational_inference computational_statistics statistical_mechanics xing.eric jordan.michael_i. in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4a4b2728d3e1/</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:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variational_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:xing.eric"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:jordan.michael_i."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.frontiersin.org/Computational_Neuroscience/10.3389/fncom.2013.00096/abstract">
    <title>Frontiers | Missing Mass Approximations for the Partition Function of Stimulus Driven Ising Models | Frontiers in Computational Neuroscience</title>
    <dc:date>2013-07-02T14:56:21+00:00</dc:date>
    <link>http://www.frontiersin.org/Computational_Neuroscience/10.3389/fncom.2013.00096/abstract</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Ising models are routinely used to quantify the second order, functional structure of neural populations. With some recent exceptions, they generally do not include the influence of time varying stimulus drive. Yet if the dynamics of network function are to be understood, time varying stimuli must be taken into account. Inclusion of stimulus drive carries a heavy computational burden because the partition function becomes stimulus dependent and must be separately calculated for all unique stimuli observed. This potentially increases computation time by the length of the data set. Here we present an extremely fast, yet simply implemented, method for approximating the stimulus dependent partition function in minutes or seconds. Noting that the most probable spike patterns (which are few) occur in the training data, we sum partition function terms corresponding to those patterns explicitly. We then approximate the sum over the remaining patterns (which are improbable, but many) by casting it in terms of the stimulus modulated missing mass (total stimulus dependent probability of all patterns not observed in the training data). We use use a product of conditioned logistic regression models to approximate the stimulus modulated missing mass. This method has complexity of roughly O(LNN_{pat}) where is L the data length, N the number of neurons and N_{pat} the number of unique patterns in the data, contrasting with the O(L2^N ) complexity of alternate methods. Using multiple unit recordings from rat hippocampus, macaque DLPFC and cat Area 18 we demonstrate our method requires orders of magnitude less computation time than Monte Carlo methods and can approximate the stimulus driven partition function more accurately than either Monte Carlo methods or deterministic approximations. This advance allows stimuli to be easily included in Ising models making them suitable for studying population based stimulus encoding."]]></description>
<dc:subject>to:NB heard_the_talk kith_and_kin haslinger.rob computational_statistics exponential_families neuroscience neural_coding_and_decoding statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6abffa0eb4e8/</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:heard_the_talk"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:haslinger.rob"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neuroscience"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_coding_and_decoding"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1306.3061">
    <title>[1306.3061] Searching for collective behavior in a network of real neurons</title>
    <dc:date>2013-06-17T18:26:03+00:00</dc:date>
    <link>http://arxiv.org/abs/1306.3061</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such "K-pairwise" models--being systematic extensions of the previously used pairwise Ising models--provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population's capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction."]]></description>
<dc:subject>to:NB neural_data_analysis neural_coding_and_decoding exponential_families bialek.william statistics neuroscience</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1144712066f0/</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:neural_coding_and_decoding"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bialek.william"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neuroscience"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aos/1366980556">
    <title>Shalizi , Rinaldo : Consistency under sampling of exponential random graph models</title>
    <dc:date>2013-04-26T15:02:50+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aos/1366980556</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling, or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM’s expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses."

--- Open version: http://arxiv.org/abs/1111.3054]]></description>
<dc:subject>in_NB have_written exponential_families exponential_family_random_graphs network_data_analysis blogged statistics stochastic_processes estimation re:your_favorite_ergm_sucks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ca93c18cfb07/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_written"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_family_random_graphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:blogged"/>
	<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:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:your_favorite_ergm_sucks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aos/1359987526">
    <title>Dou , Pollard , Zhou : Estimation in functional regression for general exponential families</title>
    <dc:date>2013-02-18T19:11:07+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aos/1359987526</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation are established. The estimators that achieve the optimal rates are constructed by constrained maximum likelihood estimation with parameters whose dimension grows with sample size. A change-of-measure argument, inspired by Le Cam’s theory of asymptotic equivalence, is used to eliminate the bias caused by the nonlinearity of exponential family models."]]></description>
<dc:subject>to:NB regression exponential_families functional_data_analysis statistics pollard.david</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:476ca957d930/</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:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:functional_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:pollard.david"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1207.4814">
    <title>[1207.4814] Automorphism Groups of Graphical Models and Lifted Variational Inference</title>
    <dc:date>2012-07-31T01:35:57+00:00</dc:date>
    <link>http://arxiv.org/abs/1207.4814</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group provides a precise mathematical framework for lifted inference in the general exponential family. Its group action partitions the set of random variables and feature functions into equivalent classes (called orbits) having identical marginals and expectations. Then the inference problem is effectively reduced to that of computing marginals or expectations for each class, thus avoiding the need to deal with each individual variable or feature. We demonstrate the usefulness of this general framework in lifting two classes of variational approximation for MAP inference: local LP relaxation and local LP relaxation with cycle constraints; the latter yields the first lifted inference that operate on a bound tighter than local constraints. Initial experimental results demonstrate that lifted MAP inference with cycle constraints achieved the state of the art performance, obtaining much better objective function values than local approximation while remaining relatively efficient."]]></description>
<dc:subject>to:NB graphical_models exponential_families identifiability statistics algebra</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:60d94b6ef329/</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:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:identifiability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:algebra"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6208875">
    <title>Sequential Anomaly Detection in the Presence of Noise and Limited Feedback</title>
    <dc:date>2012-07-13T00:46:37+00:00</dc:date>
    <link>http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6208875</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper describes a methodology for detecting anomalies from sequentially observed and potentially noisy data. The proposed approach consists of two main elements: 1) filtering, or assigning a belief or likelihood to each successive measurement based upon our ability to predict it from previous noisy observations and 2) hedging, or flagging potential anomalies by comparing the current belief against a time-varying and data-adaptive threshold. The threshold is adjusted based on the available feedback from an end user. Our algorithms, which combine universal prediction with recent work on online convex programming, do not require computing posterior distributions given all current observations and involve simple primal-dual parameter updates. At the heart of the proposed approach lie exponential-family models which can be used in a wide variety of contexts and applications, and which yield methods that achieve sublinear per-round regret against both static and slowly varying product distributions with marginals drawn from the same exponential family. Moreover, the regret against static distributions coincides with the minimax value of the corresponding online strongly convex game. We also prove bounds on the number of mistakes made during the hedging step relative to the best offline choice of the threshold with access to all estimated beliefs and feedback signals. We validate the theory on synthetic data drawn from a time-varying distribution over binary vectors of high dimensionality, as well as on the Enron email dataset."

ungated; http://arxiv.org/abs/0911.2904]]></description>
<dc:subject>statistics time_series statistical_inference_for_stochastic_processes information_theory exponential_families anomaly_detection raginsky.maxim to:blog have_read kith_and_kin ia!_ia!_raginsky_fhtagn! willett.rebecca_m.</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5e48618c116b/</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:time_series"/>
	<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:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:anomaly_detection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:raginsky.maxim"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:blog"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ia!_ia!_raginsky_fhtagn!"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:willett.rebecca_m."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.bj/1340887006">
    <title>Lockhart : Conditional limit laws for goodness-of-fit tests</title>
    <dc:date>2012-06-28T13:06:44+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.bj/1340887006</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study the conditional distribution of goodness of fit statistics of the Cramér–von Mises type given the complete sufficient statistics in testing for exponential family models. We show that this distribution is close, in large samples, to that given by parametric bootstrapping, namely, the unconditional distribution of the statistic under the value of the parameter given by the maximum likelihood estimate. As part of the proof, we give uniform Edgeworth expansions of Rao–Blackwell estimates in these models."]]></description>
<dc:subject>goodness-of-fit bootstrap statistics exponential_families in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1f0347905cdf/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:goodness-of-fit"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bootstrap"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1206.5036">
    <title>[1206.5036] Estimating Densities with Non-Parametric Exponential Families</title>
    <dc:date>2012-06-26T13:52:23+00:00</dc:date>
    <link>http://arxiv.org/abs/1206.5036</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate probability mass in the neighborhood of the observed points, resulting in a non-parametric model similar to kernel density estimators. We show that under mild conditions, the resulting model uses only the sufficient statistics if the density is within the chosen exponential family, and asymptotically, it approximates densities outside of the chosen exponential family. Using the proposed approach, we modify the exponential random graph model, commonly used for modeling small-size graph distributions, to address the well-known issue of model degeneracy."]]></description>
<dc:subject>density_estimation exponential_families exponential_family_random_graphs kirshner.sergey sufficiency statistics nonparametrics have_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:266a70b1c778/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_family_random_graphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kirshner.sergey"/>
	<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:nonparametrics"/>
	<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/1206.2689">
    <title>[1206.2689] Approximation algorithms for the normalizing constant of Gibbs distributions</title>
    <dc:date>2012-06-23T15:02:43+00:00</dc:date>
    <link>http://arxiv.org/abs/1206.2689</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Consider a family of distributions indexed by a parameter beta, where the probability that the configuration x is chosen is proportional to exp(-beta H(x)) / Z(beta). Here Z(beta) is the proper normalizing constant, equal to the sum over x' of exp(-beta H(x')). Then {pi_beta} is known as a Gibbs distribution, and Z(beta) is the partition function. This work presents a new method for approximating the partition function to a specified level of relative accuracy using only a number of samples that is O(ln(Z(beta)) ln(ln(Z(beta)))) when Z(0) >= 1. This is a sharp improvement over previous similar approaches, which used a much more complicated algorithm requiring O(ln(Z(beta)) ln(ln(Z(beta)))^5) samples."]]></description>
<dc:subject>statistical_mechanics exponential_families computational_statistics monte_carlo in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a333ae51b995/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:monte_carlo"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1206.3985">
    <title>[1206.3985] Computing the Cramer-Rao bound of Markov random field parameters: Application to the Ising and the Potts models</title>
    <dc:date>2012-06-19T14:33:48+00:00</dc:date>
    <link>http://arxiv.org/abs/1206.3985</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper addresses the problem of computing the Cramer-Rao bound for the parameters of a Markov random field. This bound depends on the derivatives of a likelihood distribution that is generally intractable. It is established that by exploiting a property of the exponential family, this intractable bound can be related to the statistical moments of the Gibbs potential of the Markov random field. A derivative-free Monte Carlo algorithm is then proposed to estimate this moments and compute the bound. To illustrate the interest of this method, the proposed algorithm is successfully applied to the Ising and Potts models. The resulting bounds are used to assess the performance of three state-of-the art estimators of the parameter of these Markov random fields."]]></description>
<dc:subject>spatial_statistics random_fields markov_models fisher_information exponential_families statistics in_NB cramer-rao_inequality</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8d34c4c6630e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:fisher_information"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cramer-rao_inequality"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/0804.3010">
    <title>[0804.3010] Generalized SURE for Exponential Families: Applications to Regularization</title>
    <dc:date>2012-06-10T22:14:29+00:00</dc:date>
    <link>http://arxiv.org/abs/0804.3010</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Stein's unbiased risk estimate (SURE) was proposed by Stein for the independent, identically distributed (iid) Gaussian model in order to derive estimates that dominate least-squares (LS). In recent years, the SURE criterion has been employed in a variety of denoising problems for choosing regularization parameters that minimize an estimate of the mean-squared error (MSE). However, its use has been limited to the iid case which precludes many important applications. In this paper we begin by deriving a SURE counterpart for general, not necessarily iid distributions from the exponential family. This enables extending the SURE design technique to a much broader class of problems. Based on this generalization we suggest a new method for choosing regularization parameters in penalized LS estimators. We then demonstrate its superior performance over the conventional generalized cross validation approach and the discrepancy method in the context of image deblurring and deconvolution. The SURE technique can also be used to design estimates without predefining their structure. However, allowing for too many free parameters impairs the performance of the resulting estimates. To address this inherent tradeoff we propose a regularized SURE objective. Based on this design criterion, we derive a wavelet denoising strategy that is similar in sprit to the standard soft-threshold approach but can lead to improved MSE performance."]]></description>
<dc:subject>statistics exponential_families estimation in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:63eac3ec2507/</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:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://ba.stat.cmu.edu/journal/2012/vol07/issue02/rousseau.pdf">
    <title>Posterior Concentration Rates for Infinite Dimensional Exponential Families</title>
    <dc:date>2012-06-07T15:56:12+00:00</dc:date>
    <link>http://ba.stat.cmu.edu/journal/2012/vol07/issue02/rousseau.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[" we derive adaptive non-parametric rates of concentration of the posterior distributions for the density model on the class of Sobolev and Besov spaces. For this purpose, we build prior models based on wavelet or Fourier expansions of the logarithm of the density. The prior models are not necessarily Gaussian."]]></description>
<dc:subject>to_read exponential_families bayesian_consistency nonparametrics statistics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:31c2704cf514/</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:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bayesian_consistency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.ejs/1328280900">
    <title>Okabayashi , Geyer : Long range search for maximum likelihood in exponential families</title>
    <dc:date>2012-02-03T19:34:28+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.ejs/1328280900</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Exponential families are often used to model data sets with complex dependence. Maximum likelihood estimators (MLE) can be difficult to estimate when the likelihood is expensive to compute. Markov chain Monte Carlo (MCMC) methods based on the MCMC-MLE algorithm in [17] are guaranteed to converge in theory under certain conditions when starting from any value, but in practice such an algorithm may labor to converge when given a poor starting value. We present a simple line search algorithm to find the MLE of a regular exponential family when the MLE exists and is unique. The algorithm can be started from any initial value and avoids the trial and error experimentation associated with calibrating algorithms like stochastic approximation. Unlike many optimization algorithms, this approach utilizes first derivative information only, evaluating neither the likelihood function itself nor derivatives of higher order than first. We show convergence of the algorithm for the case where the gradient can be calculated exactly. When it cannot, it has a particularly convenient form that is easily estimable with MCMC, making the algorithm still useful to a practitioner."]]></description>
<dc:subject>statistics exponential_families exponential_family_random_graphs network_data_analysis estimation monte_carlo optimization in_NB geyer.charles_j.</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:70fc4a382c1e/</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:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_family_random_graphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:monte_carlo"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:geyer.charles_j."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1111.3054">
    <title>[1111.3054] Consistency under Sampling of Exponential Random Graph Models</title>
    <dc:date>2011-11-15T01:51:36+00:00</dc:date>
    <link>http://arxiv.org/abs/1111.3054</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling, or, in terms of the theory of stochastic processes, that it defines a projective family. Focussing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM's expressive power. These results are actually special cases of more general ones about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses."]]></description>
<dc:subject>in_NB self-promotion exponential_family_random_graphs exponential_families statistical_inference_for_stochastic_processes statistics network_data_analysis re:your_favorite_ergm_sucks estimation large_deviations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:91aa839dd6dc/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:self-promotion"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_family_random_graphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<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:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:your_favorite_ergm_sucks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_deviations"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1111.0483">
    <title>[1111.0483] Optimally approximating exponential families</title>
    <dc:date>2011-11-04T18:23:42+00:00</dc:date>
    <link>http://arxiv.org/abs/1111.0483</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This article studies exponential families $mathcal{E}$ on finite sets such that the information divergence $D(P|mathcal{E})$ of an arbitrary probability distribution from $mathcal{E}$ is bounded by some constant $D>0$. A particular class of low-dimensional exponential families that have low values of $D$ can be obtained from partitions of the state space. The main results concern optimality properties of these partition exponential families. Exponential families where $D=log(2)$ are studied in detail. This case is special, because if $D<log(2)$, then $mathcal{E}$ contains all probability measures with full support."]]></description>
<dc:subject>exponential_families probability information_theory approximation in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f039915389ec/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://jmlr.csail.mit.edu/proceedings/papers/v15/agarwal11b.html">
    <title>Generative Kernels for Exponential Families</title>
    <dc:date>2011-11-01T12:29:05+00:00</dc:date>
    <link>http://jmlr.csail.mit.edu/proceedings/papers/v15/agarwal11b.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we propose a family of kernels for the data distributions belonging to the exponential family. We call these kernels generative kernels because they take into account the generative process of the data. Our proposed method considers the geometry of the data distribution to build a set of efficient closed-form kernels best suited for that distribution. We compare our generative kernels on multinomial data and observe improved empirical performance across the board. Moreover, our generative kernels perform significantly better when training size is small, an important property of the generative models."]]></description>
<dc:subject>kernel_methods exponential_families machine_learning in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bf5b9568f4aa/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/0812.0449">
    <title>[0812.0449] Locally adaptive estimation methods with application to univariate time series</title>
    <dc:date>2011-07-23T14:27:32+00:00</dc:date>
    <link>http://arxiv.org/abs/0812.0449</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The paper offers a unified approach to the study of three locally adaptive estimation methods in the context of univariate time series from both theoretical and empirical points of view. A general procedure for the computation of critical values is given. The underlying model encompasses all distributions from the exponential family providing for great flexibility. The procedures are applied to simulated and real financial data distributed according to the Gaussian, volatility, Poisson, exponential and Bernoulli models. Numerical results exhibit a very reasonable performance of the methods."
]]></description>
<dc:subject>time_series statistics estimation exponential_families non-stationarity to:NB</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0ee7b4d3022f/</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:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-stationarity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.nowpublishers.com/product.aspx?product=MAL&amp;doi=2200000001">
    <title>Wainwright and Jordan: Graphical Models, Exponential Families, and Variational Inference</title>
    <dc:date>2011-07-19T13:32:51+00:00</dc:date>
    <link>http://www.nowpublishers.com/product.aspx?product=MAL&amp;doi=2200000001</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[Ungated copy: http://www.cs.berkeley.edu/~jordan/papers/wainwright-jordan-fnt.pdf
]]></description>
<dc:subject>exponential_families graphical_models statistics machine_learning expectation-maximization to_read jordan.michael_i. variational_inference wainwright.martin_j. via:mraginsky</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:38db1c0ad0f9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graphical_models"/>
	<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:expectation-maximization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:jordan.michael_i."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variational_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:wainwright.martin_j."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mraginsky"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://papers.nips.cc/paper/3177-exponential-family-predictive-representations-of-state">
    <title>Exponential Family Predictive Representations of State</title>
    <dc:date>2011-04-03T00:05:13+00:00</dc:date>
    <link>https://papers.nips.cc/paper/3177-exponential-family-predictive-representations-of-state</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>to_read exponential_families machine_learning re:AoS_project tin_NB baveja.satinder_singh predictive_states</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d590e6aa33e8/</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:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:tin_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:baveja.satinder_singh"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:predictive_states"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1102.2684">
    <title>[1102.2684] Chernoff information of exponential families</title>
    <dc:date>2011-02-16T20:06:28+00:00</dc:date>
    <link>http://arxiv.org/abs/1102.2684</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>exponential_families statistics information_theory hypothesis_testing</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:38455e26536c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<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:hypothesis_testing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://jmlr.csail.mit.edu/proceedings/papers/v9/kakade10a.html">
    <title>Learning Exponential Families in High-Dimensions: Strong Convexity and Sparsity</title>
    <dc:date>2010-08-31T17:42:29+00:00</dc:date>
    <link>http://jmlr.csail.mit.edu/proceedings/papers/v9/kakade10a.html</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>density_estimation exponential_families statistics sparsity</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:18bf85dac416/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.nature.com/nature/journal/v466/n7306/abs/nature09178.html">
    <title>Sparse coding and high-order correlations in fine-scale cortical networks : Nature : Nature Publishing Group</title>
    <dc:date>2010-07-28T18:01:38+00:00</dc:date>
    <link>http://www.nature.com/nature/journal/v466/n7306/abs/nature09178.html</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>neural_data_analysis exponential_families to_read to:NB neural_coding_and_decoding</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e0df9320e47f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_coding_and_decoding"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/0903.0127">
    <title>[0903.0127] Prediction of spatio-temporal patterns of neural activity from pairwise correlations</title>
    <dc:date>2010-05-03T12:48:06+00:00</dc:date>
    <link>http://arxiv.org/abs/0903.0127</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>markov_models random_fields exponential_families neural_data_analysis functional_connectivity</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:25d705b693da/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:functional_connectivity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1003.3157">
    <title>[1003.3157] Entropy-based parametric estimation of spike train statistics</title>
    <dc:date>2010-03-17T15:36:17+00:00</dc:date>
    <link>http://arxiv.org/abs/1003.3157</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[Not sure there's anything new here...
]]></description>
<dc:subject>exponential_families neural_data_analysis</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e78c9e55eddb/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_data_analysis"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1003.0696">
    <title>[1003.0696] Exponential Family Hybrid Semi-Supervised Learning</title>
    <dc:date>2010-03-04T16:53:07+00:00</dc:date>
    <link>http://arxiv.org/abs/1003.0696</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>semi-supervised_learning statistics exponential_families re:naive-semi-supervised</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ce6c331dbd29/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:semi-supervised_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:naive-semi-supervised"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1001.3742">
    <title>[1001.3742] Functional Regression for General Exponential Families</title>
    <dc:date>2010-01-22T05:15:18+00:00</dc:date>
    <link>http://arxiv.org/abs/1001.3742</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>statistics regression nonparametrics exponential_families minimax</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e852c22baf4b/</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:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:minimax"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://people.ee.duke.edu/~maxim/pubs/raginsky_marcia_silva_willett_JMLR09.pdf">
    <title>Sequential Anomaly Detection in the Presence of Noise and Limited Feedback (Raginsky et al., submitted 2009)</title>
    <dc:date>2009-11-17T13:11:10+00:00</dc:date>
    <link>http://people.ee.duke.edu/~maxim/pubs/raginsky_marcia_silva_willett_JMLR09.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[FHTAGN!
]]></description>
<dc:subject>statistics time_series statistical_inference_for_stochastic_processes information_theory exponential_families anomaly_detection raginsky.maxim to:blog have_read in_NB willett.rebecca_m.</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2c5b58e12ff1/</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:time_series"/>
	<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:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:anomaly_detection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:raginsky.maxim"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:blog"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:willett.rebecca_m."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/0910.5561">
    <title>[0910.5561] Distinguishing Cause and Effect via Second Order Exponential Models</title>
    <dc:date>2009-11-06T01:18:50+00:00</dc:date>
    <link>http://arxiv.org/abs/0910.5561</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>causal_inference graphical_models exponential_families janzing.dominik heard_the_talk</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:45718f1ec575/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:janzing.dominik"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:heard_the_talk"/>
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</item>
<item rdf:about="http://people.ee.duke.edu/~willett/papers/raginsky_marcia_silva_willett_ISIT09.pdf">
    <title>Sequential Probability Assignment Via Online Convex Programming Using Exponential Families (Raginsky, Marcia, Silva and Willett)</title>
    <dc:date>2009-10-27T04:26:29+00:00</dc:date>
    <link>http://people.ee.duke.edu/~willett/papers/raginsky_marcia_silva_willett_ISIT09.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[Today's seminar.  Very cool.
]]></description>
<dc:subject>have_read statistics statistical_inference_for_stochastic_processes exponential_families information_theory prediction minimax optimization to:blog raginsky.maxim online_learning in_NB willett.rebecca_m. low-regret_learning</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ccb45ba35efd/</dc:identifier>
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	<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:exponential_families"/>
	<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:minimax"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:blog"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:raginsky.maxim"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:online_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:willett.rebecca_m."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:low-regret_learning"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/0904.3132">
    <title>[0904.3132] Posterior Inference in Curved Exponential Families under Increasing Dimensions</title>
    <dc:date>2009-04-22T23:47:06+00:00</dc:date>
    <link>http://arxiv.org/abs/0904.3132</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>statistics exponential_families re:bayes_as_evol in_NB</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0333d9ae4a8c/</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:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:bayes_as_evol"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;page=toc&amp;handle=euclid.lnms/1215466757">
    <title>Lawrence D. Brown Fundamentals of statistical exponential families with applications in statistical decision theory</title>
    <dc:date>2009-02-18T03:57:22+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;page=toc&amp;handle=euclid.lnms/1215466757</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[The classic monograph free online (scanned PDF, with the original UGLY pre-latex typography).
]]></description>
<dc:subject>exponential_families statistics books:recommended brown.lawrence</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:cdd2eec15bc9/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:recommended"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:brown.lawrence"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/0901.0026">
    <title>[0901.0026] On the Geometry of Discrete Exponential Families with Application to Exponential Random Graph Models</title>
    <dc:date>2009-02-06T20:57:05+00:00</dc:date>
    <link>http://arxiv.org/abs/0901.0026</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>exponential_families network_data_analysis kith_and_kin algebraic_statistics re:XV_for_networks rinaldo.alessandro have_skimmed fienberg.stephen_e.</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b7c0d39acda3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:algebraic_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:XV_for_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:rinaldo.alessandro"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_skimmed"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:fienberg.stephen_e."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aos/1009210550">
    <title>Stratified exponential families: Graphical models and model selection</title>
    <dc:date>2009-01-11T20:22:43+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aos/1009210550</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>graphical_models exponential_families latent_variables</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:65bc3eebc64a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:latent_variables"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.jstor.org/sici?sici=0090-5364(199112)19:4%3C2284:CAODFB%3E2.0.CO%3B2-R&amp;origin=MSN">
    <title>Correction: Approximation of Density Functions by Sequences of Exponential Families - JSTOR: The Annals of Statistics, Vol. 19, No. 4 (Dec., 1991 ), pp. 2284-2284</title>
    <dc:date>2008-06-04T16:06:22+00:00</dc:date>
    <link>http://www.jstor.org/sici?sici=0090-5364(199112)19:4%3C2284:CAODFB%3E2.0.CO%3B2-R&amp;origin=MSN</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>statistics exponential_families density_estimation sheu.chyong-hwa barron.andrew_w.</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0dd8a6fc9133/</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:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sheu.chyong-hwa"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:barron.andrew_w."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.aos/1176348252">
    <title>Approximation of Density Functions by Sequences of Exponential Families - Barron and Sheu</title>
    <dc:date>2008-06-04T16:04:48+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.aos/1176348252</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>statistics exponential_families density_estimation sheu.chyong-hwa barron.andrew_w.</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c6b7120b945e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sheu.chyong-hwa"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:barron.andrew_w."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.jstatsoft.org/v24">
    <title>Journal of Statistical Software — Special Issue on Statnet</title>
    <dc:date>2008-05-20T18:37:48+00:00</dc:date>
    <link>http://www.jstatsoft.org/v24</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[yay, free, statistically-sound software for modeling network structures!
]]></description>
<dc:subject>network_data_analysis computational_statistics exponential_families morris.martina goodreau.steven_m bender-de_moll.skye moody.james handcock.mark butts.carter_t. hunter.david_r.</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:edb19fc0d47b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:morris.martina"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:goodreau.steven_m"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bender-de_moll.skye"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:moody.james"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:handcock.mark"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:butts.carter_t."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hunter.david_r."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://stat.gamma.rug.nl/snijders/cup_ch11.pdf">
    <title>Models for Longitudinal Network Data</title>
    <dc:date>2008-04-21T21:24:25+00:00</dc:date>
    <link>http://stat.gamma.rug.nl/snijders/cup_ch11.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[Includes "actor-oriented" models in the general exponential family random graph framework.
]]></description>
<dc:subject>network_data_analysis exponential_families markov_models to_teach:complexity-and-inference snijders.t.a.b.</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c0836b874717/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:complexity-and-inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:snijders.t.a.b."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://math.yale.edu/mandelbrot/web_pdfs/029sufficiencyandestimation.pdf">
    <title>The Role of Sufficiency and of Estimation in Thermodynamics (Mandelbrot, 1962)</title>
    <dc:date>2008-02-29T02:14:01+00:00</dc:date>
    <link>http://math.yale.edu/mandelbrot/web_pdfs/029sufficiencyandestimation.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[Free reprint of paper earlier saved in JSTOR version.  Zeroth law = conditional on a sufficient statistic, the parameter doesn't change the temperature, etc.
]]></description>
<dc:subject>statistics statistical_mechanics exponential_families sufficiency gibbs_distributions mandelbrot.benoit</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f03a05393136/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:gibbs_distributions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mandelbrot.benoit"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://links.jstor.org/sici?sici=0003-4851(196209)33%3A3%3C1021%3ATROSAO%3E2.0.CO%3B2-N">
    <title>The Role of Sufficiency and of Estimation in Thermodynamics (Mandelbrot, 1962)</title>
    <dc:date>2008-02-28T15:32:42+00:00</dc:date>
    <link>http://links.jstor.org/sici?sici=0003-4851(196209)33%3A3%3C1021%3ATROSAO%3E2.0.CO%3B2-N</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[_Very_ nice.  Zeroth law = you only need to worry about sufficient statistics; etc.
]]></description>
<dc:subject>statistics statistical_mechanics exponential_families sufficiency gibbs_distributions mandelbrot.benoit</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:86abd11226a8/</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_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sufficiency"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mandelbrot.benoit"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/0708.3411">
    <title>[0708.3411] On causally asymmetric versions of Occam's Razor and their relation to thermodynamics</title>
    <dc:date>2007-11-22T04:36:05+00:00</dc:date>
    <link>http://arxiv.org/abs/0708.3411</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>thermodynamics causality occams_razor to:blog arrow_of_time exponential_families have_read janzing.dominik</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:960c927165bd/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:thermodynamics"/>
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    <title>[0709.0447] Local mixture models of exponential families</title>
    <dc:date>2007-11-15T13:58:48+00:00</dc:date>
    <link>http://arxiv.org/abs/0709.0447</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>statistics exponential_families mixture_models in_NB</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a2373dda5549/</dc:identifier>
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