Statistical inference with probabilistic graphical models

摘要

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, tillFriday October 11th, 2013. The school was organized by Florent Krzakala fromUPMC & ENS Paris, Federico Ricci-Tersenghi from La Sapienza Roma, LenkaZdeborova from CEA Saclay & CNRS, and Riccardo Zecchina from PolitecnicoTorino. This lecture of Devavrat Shah (MIT) covers the basics of inference andlearning. It explains how inference problems are represented within structuresknown as graphical models. The theoretical basis of the belief propagationalgorithm is then explained and derived. This lecture sets the stage forgeneralizations and applications of message passing algorithms.