Stochastic approximation learning for mixtures of multivariate elliptical distributions

Most of the current approaches to mixture modeling consider mixture components from a few families of probability distributions, in particular from the Gaussian family. The reasons of these preferences can be traced to their training algorithms, typically versions of the Expectation-Maximization (EM) method. The re-estimation equations needed by this method become very complex as the mixture components depart from the simplest cases. Here we propose to use a stochastic approximation method for probabilistic mixture learning. Under this method it is straightforward to train mixtures composed by a wide range of mixture components from different families. Hence, it is a flexible alternative for mixture learning. Experimental results are presented to show the probability density and missing value estimation capabilities of our proposal.

Research highlights
► Stochastic approximation is proposed as an alternative to EM for probabilistic mixture learning.
► Non standard probability density functions are easily managed.
► The multivariate triangular family of probability density functions is presented.
► Multivariate triangular pdfs feature a finite support and a linearly decaying density.
► Differences among probability density function families are studied.