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We study the problem of learning a mixture model of non-parametric productdistributions. The problem of learning a mixture model is that of finding thecomponent distributions along with the mixing weights using observed samplesgenerated from the mixture. The problem is well-studied in the parametricsetting, i.e., when the component distributions are members of a parametricfamily -- such as Gaussian distributions. In this work, we focus onmultivariate mixtures of non-parametric product distributions and propose atwo-stage approach which recovers the component distributions of the mixtureunder a smoothness condition. Our approach builds upon the identifiabilityproperties of the canonical polyadic (low-rank) decomposition of tensors, intandem with Fourier and Shannon-Nyquist sampling staples from signalprocessing. We demonstrate the effectiveness of the approach on synthetic andreal datasets.

Learning Mixtures of Smooth Product Distributions: Identifiability and Algorithm