2016
Jun
14

# Dynamics & probability: Amitai Zernik (HUJI): A Diagrammatic Recipe for Computing Maxent Distributions

2:00pm to 3:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Room 209)

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.

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.