  Effective non-parametric density estimation is a key challenge in
high-dimensional multivariate data analysis. In this paper,we propose a novel
approach that builds upon tensor factorization tools. Any multivariate density
can be represented by its characteristic function, via the Fourier transform.
If the sought density is compactly supported, then its characteristic function
can be approximated, within controllable error, by a finite tensor of leading
Fourier coefficients, whose size de-pends on the smoothness of the underlying
density. This tensor can be naturally estimated from observed realizations of
the random vector of interest, via sample averaging. In order to circumvent the
curse of dimensionality, we introduce a low-rank model of this characteristic
tensor, which significantly improves the density estimate especially for
high-dimensional data and/or in the sample-starved regime. By virtue of
uniqueness of low-rank tensor decomposition, under certain conditions, our
method enables learning the true data-generating distribution. We demonstrate
the very promising performance of the proposed method using several measured
datasets.
