Bayesian inference as iterated random functions with applications to sequential inference in graphical models

Part of Advances in Neural Information Processing Systems 26 (NIPS 2013)

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Arash Amini, XuanLong Nguyen


We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is presented. As an application of the general theory we analyze convergence behaviors of exact and approximate message-passing algorithms that arise in a sequential change point detection problem formulated via a latent variable directed graphical model. The sequential inference algorithm and its supporting theory are illustrated by simulated examples.