Tropical Geometry of Statistical Models

Details Tropical Geometry of Statistical Models Tropical Geometry of Statistical Models

2003-11-08

arxiv.org/abs/q-bio/0311009v2

Biology

Quantitative Biology

Quantitative Methods

14 pages, 3 figures. Major revision. Applications now in companion paper, "Parametric Inference for Biological Sequence Analys

Scientific paper

10.1073/pnas.0406010101

This paper 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. The question addressed here is how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. A key role is played by the Newton polytope of a statistical model. Our results are applied to the hidden Markov model and to the general Markov model on a binary tree.

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