Let S be a finite set (the sample space), and f_i: S -> R functions, for 1 ≤ i ≤ k. Given a k-tuple (v_1,...,v_k) in R^k it is natural to ask: What is the distribution P on S that maximizes the entropy -Σ P(x) log(P(x)) subject to the constraint that the expectation of f_i be v_i? In this talk I'll discuss a closed formula for the solution P in terms of a sum over cumulant trees. This is based on a general calculus for solving perturbative optimization problems due to Feynman, which may be of interest in its own right. The talk will be completely self-contained, requiring only rudimentary knowledge of calculus and probability theory. This is joint work with Tomer Schlank and Ran Tessler.
Tue, 14/06/2016 - 14:00 to 15:00
Manchester building, Hebrew University of Jerusalem, (Room 209)