Variational Learning for Switching State-Space Models

摘要: We introduce a new statistical model for time series that iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each these regimes. This combines generalizes two most widely used stochastic time-series models— hidden Markov models dynamical systems—and is closely related to are in control econometrics literatures. It can also be derived by extending mixture experts neural network (Jacobs, Jordan, Nowlan, & Hinton, 1991) its fully version, which both expert gating networks recurrent. Inferring posterior probabilities states this computationally intractable, therefore exact expectation maximization (EM) algorithm cannot applied. However, we present variational approximation maximizes lower bound on log-likelihood makes use forward backward recursions Kalman filter systems. tested artificial sets natural set respiration force from patient sleep apnea. The results suggest approximations viable method inference learning switching state-space models.