Sequential Inference for Factorial Changepoint Models

Conditional Gaussian changepoint models are an interesting subclass of jump-Markov dynamic linear systems, in which, unlike the majority of such intractable hybrid models, exact inference is achievable in polynomial time. However, many applications of interest involve several simultaneously unfolding processes with occasional regime switches and shared observations. In such scenarios, a factorial model, where each process is modelled by a changepoint model is more natural. In this paper, we derive a sequential Monte Carlo algorithm, reminiscent to the Mixture Kalman filter (MKF) [1]. However, unlike MKF, the factorial structure of our model prohibits the computation of the posterior filtering density (the optimal proposal distribution). Even evaluating the likelihood conditioned on a few switch configurations can be time consuming. Therefore, we derive a propagation algorithm (upward-downward) that exploits the factorial structure of the model and facilitates computing Kalman filtering recursions in information form without the need for inverting large matrices. To motivate the utility of the model, we illustrate our approach on a large model for polyphonic pitch tracking.