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We present an alternating least squares type numerical optimization scheme toestimate conditionally-independent mixture models in $\mathbb{R}^n$, withoutparameterizing the distributions. Following the method of moments, we tackle anincomplete tensor decomposition problem to learn the mixing weights andcomponentwise means. Then we compute the cumulative distribution functions,higher moments and other statistics of the component distributions throughlinear solves. Crucially for computations in high dimensions, the steep costsassociated with high-order tensors are evaded, via the development of efficienttensor-free operations. Numerical experiments demonstrate the competitiveperformance of the algorithm, and its applicability to many models andapplications. Furthermore we provide theoretical analyses, establishingidentifiability from low-order moments of the mixture and guaranteeing locallinear convergence of the ALS algorithm.

Moment Estimation for Nonparametric Mixture Models Through Implicit Tensor Decomposition