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 optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances -including the key problems of computing marginals and modes of probability distributions -- are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varie...

• Type: Journal
• Year: 2008
• Where: FTML
• Authors: Martin J. Wainwright, Michael I. Jordan
• Keywords: FTML 2008, Graphical Models, Multivariate Statistical Models, Probabilistic Graphical Models