Belief Propagation is an approximation widely used in the inference of discrete graphical models. It has been derived many times in different fields, and is also known as SumProduct algorithm (computer science) or Cavity equations (in physics).
This seminar explores the multifaceted nature of Belief Propagation (BP) and its wide-ranging applications. We begin with a high school-level derivation of BP from Bayes' formula, providing an accessible entry point to this powerful algorithm. The discussion then delves into the connection between BP and free energy, offering a variational derivation that bridges the conceptual approaches in physics and mathematics. We examine the relationship between BP and the Cavity Method, touching upon replica theory and graph colouring - topics that contributed to Giorgio Parisi's Nobel Prize-winning work. Building on the concept of graphical models, we introduce generalizations of Belief Propagation, expanding messages to flow between larger groups of variables. The latter part of the seminar focuses on practical applications in biology, demonstrating BP's utility in three key areas: inferring epidemic dynamics, identifying contamination sources, and reconstructing ancestral protein sequences. This comprehensive overview aims to illuminate the interdisciplinary nature of Belief Propagation, showcasing its roots in statistical physics and mathematics, and its powerful applications in solving complex biological problems. Attendees will gain insights into how this algorithm connects diverse fields and offers innovative solutions to challenging inference tasks in the life sciences.
