Algebraic statistical models

By Mathias Drton, Seth Sullivant. 2007

58 citations recorded by the source corpus.

Many statistical models are algebraic in that they are defined in terms of polynomial constraints, or in terms of polynomial or rational parametrizations. The parameter spaces of such models are typically semi-algebraic subsets of the parameter space of a reference model with nice properties, such as for example a regular exponential family. This observation leads to the definition of an `algebraic exponential family'. This new definition provides a unified framework for the study of statistical models with algebraic structure. In this paper we review the ingredients to this definition and illustrate in examples how computational algebraic geometry can be used to solve problems arising in statistical inference in algebraic models.

Subfields: Algebra and Number Theory, Computational Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/281617d47dd46999fc6114ea1d7cc4d4b7127127

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In Algebra and Number Theory

In Computational Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Geometry of the Restricted Boltzmann Machine (2009, background): “This class of algebraic statistical models includes graphical models for both Gaussian and discrete random variables [11, 13].”
Discrete chain graph models (2009, background): “This paper investigates smoothness properties of discrete models of type II, III and IV, which are all algebraic exponential families in the sense of [9].”
Likelihood ratio tests and singularities (2007, background): “Examples in which Chernoff-regularity fails and the likelihood ratio statistic λn does not converge in distribution can be found in [9] and [14].”