dorsal/arxiv
View SchemaTropical Geometry of Statistical Models
| Authors | Lior Pachter, Bernd Sturmfels |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0311009 |
| URL | https://arxiv.org/abs/q-bio/0311009 |
| DOI | 10.1073/pnas.0406010101 |
Abstract
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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"abstract": "This paper presents a unified mathematical framework for inference in\ngraphical models, building on the observation that graphical models are\nalgebraic varieties.\n From this geometric viewpoint, observations generated from a model are\ncoordinates of a point in the variety, and the sum-product algorithm is an\nefficient tool for evaluating specific coordinates. The question addressed here\nis how the solutions to various inference problems depend on the model\nparameters. The proposed answer is expressed in terms of tropical algebraic\ngeometry. A key role is played by the Newton polytope of a statistical model.\nOur results are applied to the hidden Markov model and to the general Markov\nmodel on a binary tree.",
"arxiv_id": "q-bio/0311009",
"authors": [
"Lior Pachter",
"Bernd Sturmfels"
],
"categories": [
"q-bio.QM",
"math.AG",
"q-bio.GN"
],
"doi": "10.1073/pnas.0406010101",
"title": "Tropical Geometry of Statistical Models",
"url": "https://arxiv.org/abs/q-bio/0311009"
},
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"type": "Model",
"variant": "snapshot-2026-03-01",
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