Belief Propagation on Graphs

This lecture introduces the concept of belief propagation on graphs, focusing on computing the partition function and free energy of statistical physics models. The instructor explains how to iterate the belief propagation equations on trees and extends the method to loopy graphs, discussing the challenges and heuristics involved. The lecture delves into the computation of free entropy and the implications of the independence assumption in incoming messages. It also explores the application of belief propagation on sparse random graphs, highlighting the significance of long loops in such graphs. The instructor demonstrates how the expected length of loops in sparse random graphs grows logarithmically with the graph size, providing insights into the feasibility and limitations of belief propagation algorithms.