Graphical Models, Exponential Families, and Variational Inference
نویسندگان
چکیده
منابع مشابه
Graphical Models, Exponential Families, and Variational Inference
The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimizati...
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We provide a classi cation of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks with several families of local distributions, are curved exponential families ...
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Markov Random Fields, or undirected graphical models are widely used to model highdimensional multivariate data. Classical instances of these models, such as Gaussian Graphical and Ising Models, as well as recent extensions (Yang et al., 2012) to graphical models specified by univariate exponential families, assume all variables arise from the same distribution. Complex data from high-throughpu...
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We provide a classi cation of graphical models according to their representation as exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical (DAG) models and chain graphs with no hidden variables, including DAG models with several families of local distributions, are curved exponential families (CEFs) and graph...
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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 fea...
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ژورنال
عنوان ژورنال: Foundations and Trends® in Machine Learning
سال: 2007
ISSN: 1935-8237,1935-8245
DOI: 10.1561/2200000001