Approximate Methods for Calculating Marginals and Likelihoods

Authored by: Marloes Maathuis , Mathias Drton , Steffen Lauritzen , Martin Wainwright

Handbook of Graphical Models

Print publication date:  November  2018
Online publication date:  November  2018

Print ISBN: 9781498788625
eBook ISBN: 9780429463976
Adobe ISBN:

10.1201/9780429463976-5

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Abstract

Exact marginal inference, as discussed in the preceding Chapter , is tractable only in the simplest of models (trees, cycles, low tree width graphs, etc.). Further, marginal inference is often a basic subproblem that needs to be solved repeatedly in order to learn graphical models, that is, to fit a graphical model to a set of data observations. As a result fast, approximate inference algorithms are often necessary in practice. This chapter reviews the basic theory of variational approximations and how they can be used to design algorithms for approximate marginal inference and learning in graphical models. Closely related approximations for MAP inference are discussed in Chapter .

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