Counting contingency tablesAlgebra & Discrete Mathematics
|Speaker:||Prof. Igor Pak, Univ. of California, Los Angeles|
|Location:||1147 Math Science Building|
|Start time:||Mon, Apr 8 2019, 12:10PM|
Contingency tables are matrices with fixed row and column sums. They are in natural correspondence with bipartite multi-graphs with fixed degrees and can also be viewed as integer points in transportation polytopes. Counting and random sampling of contingency tables is a fundamental problem in statistics which remains unresolved in full generality.
In the talk, I will review both asymptotic and MCMC approaches, and then present a new Markov chain construction which provably works for sparse margins. I will conclude with the ongoing work on the phase transition for certain Barvinok margins.
Joint work with Sam Dittmer.