Variational Bayesian Inference for Hidden Markov Models With Multivariate Gaussian Output Distributions

Hidden Markov Models (HMM) are a standard technique in time series analysis or data mining. Given a (set of) time series sample data, they are typically trained by means of a special variant of an expectation maximization (EM) algorithm, the Baum-Welch algorithm. HMM are used for gesture recognition, machine tool monitoring, or speech recognition, for instance. Second-order techniques are used to find values for parameters of probabilistic models from sample data. The parameters are regarded as random variables, and distributions are defined over these variables. These type of these second-order distributions depends on the type of the underlying probabilistic models. Typically, so called conjugate distributions are chosen, e.g., a Gaussian-Wishart distribution for an underlying Gaussian for which mean and covariance matrix have to be determined. Second-order techniques have some advantages over conventional approaches, e.g.,