Mathematics ColloquiumDate: Time: 4:00 pm–4:50 pm
Local Host: Vladimir Itskov
Additional Public Info:
Abstract: Inspired by the problem of sensory coding in neuroscience, we study the maximum entropy distribution on weighted graphs with a given expected degree sequence. This distribution is characterized by independent edge weights parameterized by vertex potentials at each node. Rather surprisingly, a single graph sample suffices to determine these parameters and thus the original distribution. We explain how we arrived at this result, first proved by Chatterjee, Diaconis, and Sly for the case of unweighted (binary) graphs, and how it relates to recent work of Sanyal, Sturmfels, and Vinzant on the entropic discriminant in algebraic geometry. Interestingly, our proofs require an intricate study of the inverses of diagonally dominant positive matrices and the combinatorics of bipartite graphs. (Joint work with Shaowei Lin and Andre Wibisono).
Refreshments will be served in 348 Avery 3:30-4pm.
The talk is free and open to the public.