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Tropical geometry of statistical models.

Authors
Type
Published Article
Journal
Proceedings of the National Academy of Sciences of the United States of America
Publication Date
Volume
101
Issue
46
Pages
16132–16137
Identifiers
PMID: 15534224
Source
Medline

Abstract

This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.

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