Tropical geometry of statistical models Export

@article{citeulike:3110825, abstract = {10.1073/pnas.0406010101 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.}, author = {Pachter, Lior and Sturmfels, Bernd}, citeulike-article-id = {3110825}, citeulike-linkout-0 = {http://dx.doi.org/10.1073/pnas.0406010101}, citeulike-linkout-1 = {http://www.pnas.org/content/101/46/16132.abstract}, citeulike-linkout-2 = {http://www.pnas.org/content/101/46/16132.full.pdf}, citeulike-linkout-3 = {http://view.ncbi.nlm.nih.gov/pubmed/15534224}, citeulike-linkout-4 = {http://www.hubmed.org/display.cgi?uids=15534224}, day = {16}, doi = {10.1073/pnas.0406010101}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, keywords = {algebraic\_geometry, graphical\_models, hmm, modelling, statistics, theory}, month = {November}, number = {46}, pages = {16132--16137}, posted-at = {2008-08-12 06:43:22}, priority = {2}, title = {Tropical geometry of statistical models}, url = {http://dx.doi.org/10.1073/pnas.0406010101}, volume = {101}, year = {2004} }

TY - JOUR ID - citeulike:3110825 L3 - citeulike-article-id:3110825 N2 - 10.1073/pnas.0406010101 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. IS - 46 JF - Proceedings of the National Academy of Sciences of the United States of America EP - 16137 TI - Tropical geometry of statistical models VL - 101 SP - 16132 KW - algebraic_geometry KW - graphical_models KW - hmm KW - modelling KW - statistics KW - theory AU - Pachter, Lior AU - Sturmfels, Bernd PY - 2004/11/16/ UR - http://dx.doi.org/10.1073/pnas.0406010101 ER -