Sparse mixture models inspired by ANOVA decompositions

Inspired by the analysis of variance (ANOVA) decomposition functions, we propose a Gaussian-uniform mixture model on high-dimensional torus which relies assumption that function wish to approximate can be well explained limited variable interactions. We consider three approaches, namely wrapped Gaussians, diagonal and products von Mises distributions. The sparsity is ensured fact its summands are Gaussian-like density functions acting low-dimensional spaces uniform probability densities defined remaining directions. To learn such sparse from given samples, an objective consisting negative log-likelihood regularizer penalizes number summands. For minimizing this functional combine Expectation Maximization algorithm with proximal step takes into account. decide important, apply Kolmogorov-Smirnov test. Numerical examples demonstrate performance our approach.