  This work approximates high-dimensional density functions with an ANOVA-like
sparse structure by the mixture of wrapped Gaussian and von Mises
distributions. When the dimension $d$ is very large, it is complex and
impossible to train the model parameters by the usually known learning
algorithms due to the curse of dimensionality. Therefore, assuming that each
component of the model depends on an a priori unknown much smaller number of
variables than the space dimension $d,$ we first define an algorithm that
determines the mixture model's set of active variables by the
Kolmogorov-Smirnov and correlation test. Then restricting the learning
procedure to the set of active variables, we iteratively determine the set of
variable interactions of the marginal density function and simultaneously learn
the parameters by the Kolmogorov and correlation coefficient statistic test and
the proximal Expectation-Maximization algorithm. The learning procedure
considerably reduces the algorithm's complexity for the input dimension $d$ and
increases the model's accuracy for the given samples, as the numerical examples
show.
