A multimodal variational approach to learning and inference in switching state space models
L. Lee · 2004
An important general model for discrete-time signal processing is the switching state space (SSS) model, which generalizes the hid-den Markov model and the Gaussian state space model. Inference and parameter estimation in this model are known to be computa-tionally intractable. This paper presents a powerful new approxi-mation to the SSS model. The approximation is based on a vari-ational technique that preserves the multimodal nature of the con-tinuous state posterior distribution. Furthermore, by incorporating a windowing technique, the resulting EM algorithm has complex-ity that is just linear in the length of the time series. An alterna-tive Viterbi decoding with frame-based likelihood is also presented which is crucial for the speech application that originally motivates this work. Our experiments focus on demonstrating the effective-ness of the algorithm by extensive simulations. A typical example in speech processing is also included to show the potential of this approach for practical applications. 1.