Statistical inference with probabilistic graphical models

TL;DR

This paper provides an overview of probabilistic graphical models, explaining how inference problems are represented and detailing the belief propagation algorithm's theoretical foundations and applications.

Contribution

It offers a clear explanation of inference in graphical models and the belief propagation algorithm, setting the stage for further generalizations and applications.

Findings

Belief propagation algorithm's theoretical basis explained

Representation of inference problems using graphical models

Foundation for message-passing algorithm applications

Abstract

These are notes from the lecture of Devavrat Shah given at the autumn school "Statistical Physics, Optimization, Inference, and Message-Passing Algorithms", that took place in Les Houches, France from Monday September 30th, 2013, till Friday October 11th, 2013. The school was organized by Florent Krzakala from UPMC & ENS Paris, Federico Ricci-Tersenghi from La Sapienza Roma, Lenka Zdeborova from CEA Saclay & CNRS, and Riccardo Zecchina from Politecnico Torino. This lecture of Devavrat Shah (MIT) covers the basics of inference and learning. It explains how inference problems are represented within structures known as graphical models. The theoretical basis of the belief propagation algorithm is then explained and derived. This lecture sets the stage for generalizations and applications of message passing algorithms.