Colloquium April 25
Date: Friday April 25
Time: 14:30 to 15:30
Place: 455 McBryde (Commons Room)
Speaker: Michael Stillman of Cornell
Title: Algebraic geometry and Bayesian networks
Abstract
A Bayesian network encodes independence statements for a finite number
of discrete random variables. Bayesian networks have many
applications, including artificial intelligence and bioinformatics.
These models give rise to interesting ideals in polynomial rings,
called Markov ideals. In this talk, we describe some interesting and
important properties of these ideals and their relationship with
statistics. This leads to a link between the languages of statistics
and of algebraic geometry. For example, the algebraic analog of the
factorization theorem in Bayesian statistics leads to interesting
features of the decompositions of these algebraic sets. The algebraic
interpretation of hidden random variables leads naturally to secant
loci for projective varieties.
Markov ideals are ideals in a generally large number of variables,
which present difficult challenges for computer algebra algorithms and
systems. We describe some of the difficulties which occur, why they
are so difficult for computer algebra systems, and present some
algorithms that have been working reasonably well in practice.
We will assume very little statistics and algebraic geometry. This
talk represents joint work with Luis David Garcia and Bernd Sturmfels.
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