Bayesian Change-Point Detection via Context-Tree Weighting

Change-point detection for discrete time series is an important task with numerous applications. We develop a new hierarchical Bayesian framework for modelling inhomogeneous discrete time series with change-points. The distributions of different segments are modelled as variable-memory Markov chains, defining piece-wise homogeneous variable-memory chains. Building on the recently introduced Bayesian Context Trees framework, it is shown that the Context-Tree Weighting algorithm can be employed to compute the prior predictive likelihood of each segment, with all models and parameters integrated out. This is then used to develop a new class of effective Markov chain Monte Carlo algorithms for the posterior of the number and locations of change-points. These not only identify the most likely change-points, but also provide access to their entire posterior distribution. Estimates of the actual models in each segment can be obtained at negligible cost. Results on both synthetic and real-world data sets indicate that the proposed methodology performs better or as well as state-of-the-art techniques.