Strategies for Sequential Inference in Factorial Switching State Space Models

Factorial switching state space models are large hybrid time series models in which inference is intractable even in a single time slice. For the conditional Gaussian case, we derive a message propagation algorithm (upward-downward) that exploits the factorial structure of the model and facilitates computing messages without the need for inverting large matrices. Using the propagation algorithm as a sub-routine, we develop a Rao-Blackwellized Gibbs sampler and a variational approximation of structured mean field type to compute an approximate proposal density. These proposal are useful for both filtering or for marginal maximum a-posteriori estimates. We illustrate the utility of our approach on a large factorial state space model for polyphonic music transcription.