Mathematical Sciences Department Colloquium
Jane Coons, Max Planck Institute
Tuesday, January 28th
12-1pm
Stratton 202
Algebraic and Combinatorial Approaches to Maximum
Likelihood Estimation
In the field of algebraic statistics, we view statistical models as part of
an algebraic variety and use tools from algebra, geometry and
combinatorics to learn statistically relevant information about these
models. In this talk, we discuss the algebraic interpretation of
likelihood inference for discrete statistical models. We present recent
work on the iterative proportional scaling (IPS) algorithm, which is
used to compute the maximum likelihood estimate (MLE), and give
algebraic conditions under which this algorithm outputs the exact MLE
in one cycle. Next, we introduce quasi-independence models, which
describe the joint distribution of two random variables where some
combinations of their states cannot co-occur, but they are otherwise
independent. We combinatorially classify the quasi-independence
models whose MLEs are rational functions of the data. We show that
each of these has a parametrization which satisfies the conditions that
guarantee one-cycle convergence of the IPS algorithm