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