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On Grobner bases of Elimination and Toric Ideals describing Maximum Entropy models

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My main aim in this talk is to introduce some notions on how results from commutative algebra and algebraic geometry can be used in analysis of statistical models, in particular, maximum entropy models. First, I will give a brief introduction of Grobner bases and its applications to algebraic geometry. I will show that maximum entropy models can be described with toric ideals by embedding them in algebraic varieties (by means of the Zariski closure). Based on these ideas, I will present some algebraic methods for estimation of these models along with some applications. Finally, I will discuss some ideas and problems on certain algebraic quantities serving as complexity measures for these models.

This talk is part of the Statistics series.

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