Bayesian inference as iterated random functions with applications to sequential inference in graphical models
This work addresses sequential inference problems in graphical models, presenting a theoretical framework that is incremental in nature.
The authors tackled the problem of sequential inference in graphical models by proposing a formalism of iterated random functions with semigroup property, showing that Bayesian posterior updates are specific instances, and applied this to analyze message-passing algorithms for change point detection, with convergence theory and simulated examples.
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.