Modeling Event-driven Time Series with Generalized Hidden Semi-Markov Models

This report introduces a new model for event-driven temporal sequence processing: Generalized Hidden Semi-Markov Models (GHSMMs). GHSMMs are an extension of hidden Markov models to continuous time that builds on turning the stochastic process of hidden state traversals into a semi-Markov process. A large variety of probability distributions can be used to specify transition durations. It is shown how GHSMMs can be used to address the principle problems of temporal sequence processing: sequence generation, sequence recognition and sequence prediction. Additionally, an algorithm is described how the parameters of GHSMMs can be determined from a set of training data: The Baum-Welch algorithm is extended by an embedded expectation-maximization algorithm. Under some conditions the procedure can be simplified to the estimation of distribution moments. A proof of convergence and a complexity assessment are provided