Switch-Reset Models : Exact and Approximate Inference

Reset models are constrained switching latent Markov models in which the dynamics either continues according to a standard model, or the latent variable is resampled. We consider exact marginal inference in this class of models and their extension, the switch-reset models. A further convenient class of conjugate-exponential reset models is also discussed. For a length $T$ time-series, exact filtering scales with $T^2$ squared and smoothing $T^3$ cubed. We discuss approximate filtering and smoothing routines that scale linearly with $T$. Applications are given to change-point models and reset linear dynamical systems.