  We study the problem of learning a mixture model of non-parametric product
distributions. The problem of learning a mixture model is that of finding the
component distributions along with the mixing weights using observed samples
generated from the mixture. The problem is well-studied in the parametric
setting, i.e., when the component distributions are members of a parametric
family -- such as Gaussian distributions. In this work, we focus on
multivariate mixtures of non-parametric product distributions and propose a
two-stage approach which recovers the component distributions of the mixture
under a smoothness condition. Our approach builds upon the identifiability
properties of the canonical polyadic (low-rank) decomposition of tensors, in
tandem with Fourier and Shannon-Nyquist sampling staples from signal
processing. We demonstrate the effectiveness of the approach on synthetic and
real datasets.
