Empirical Bayesian Change Point Detection

This paper explores a Bayesian method for the detection of sudden changes in the generative parameters of a data series. The problem is phrased as a hidden Markov model, where change point locations correspond to unobserved states, which grow in number with the number of observations. Our interest lies in the marginal change point posterior density. Rather than optimize a likelihood function of model parameters, we adapt the Baum-Welch algorithm to maximize a bound on the log marginal likelihood with respect to prior hyperparameters. This empirical Bayesian approach allows scale-invariance, and can be viewed as an expectation maximization algorithm for hyperparameter optimization in conjugate exponential models with latent variables. The expectation and maximization steps make respective use of variational and concave-convex inner loops. A judicious choice of change point prior allows for fast recursive computations on a graphical model. Results are shown on a number of real-world data sets.