A Probabilistic Expectation Maximization Algorithm for Multivariate Laplacian Mixtures

Estimating parameters of mixture models is a typical application of the expectation maximization (EM) algorithm. For the family of multivariate exponential power (MEP) distributions, which is a generalization of the well known multivariate Gaussian distribution, we introduce an approximative EM algorithm, and a probabilistic variant called stochastic EM algorithm, which provides a significant speedup. We prove that, with high probability, single update steps of the probabilistic variant do not differ much from the deterministic solution, assuming certain properties of the input data set. A set of practical experiments shows that this holds true, even over multiple successive iterations.