Bayesian inference as iterated random functions with applications to sequential inference in graphical models
Machine Learning
2013-11-05 v1 Statistics Theory
Methodology
Statistics Theory
Abstract
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.
Cite
@article{arxiv.1311.0072,
title = {Bayesian inference as iterated random functions with applications to sequential inference in graphical models},
author = {Arash A. Amini and XuanLong Nguyen},
journal= {arXiv preprint arXiv:1311.0072},
year = {2013}
}