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Tropical Geometry of Statistical Models

Pachter, Lior and Sturmfels, Bernd (2004) Tropical Geometry of Statistical Models. Proceedings of the National Academy of Sciences of the United States of America, 101 (46). pp. 16132-16137. ISSN 0027-8424. PMCID PMC528960. doi:10.1073/pnas.0406010101.

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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.

Item Type:Article
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URLURL TypeDescription CentralArticle Paper
Pachter, Lior0000-0002-9164-6231
Additional Information:© 2004 The National Academy of Sciences. Communicated by Stephen E. Fienberg, Carnegie Mellon University, Pittsburgh, PA, September 10, 2004 (received for review January 25, 2004) We thank Komei Fukuda, Michael Joswig, and Kristian Ranestad for their help in obtaining the computational results reported in section 2. L.P. was supported in part by National Institutes of Health Grant R01-HG02362-02. B.S. was supported by a Hewlett Packard Visiting Research Professorship 2003/2004 at the Mathematical Sciences Research Institute (MSRI) at the University of California, Berkley, and in part by National Science Foundation Grant DMS-0200729.
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Hewlett-Packard CompanyUNSPECIFIED
Issue or Number:46
PubMed Central ID:PMC528960
Record Number:CaltechAUTHORS:20170307-073504137
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Official Citation:Lior Pachter and Bernd Sturmfels Tropical geometry of statistical models PNAS 2004 101 (46) 16132-16137; published ahead of print November 8, 2004, doi:10.1073/pnas.0406010101
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74825
Deposited By: Tony Diaz
Deposited On:07 Mar 2017 15:55
Last Modified:11 Nov 2021 05:30

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