Moment Estimation for Nonparametric Mixture Models Through Implicit Tensor Decomposition
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We present an alternating least squares type numerical optimization scheme to estimate conditionally-independent mixture models in ℝ^n, with minimal additional distributional assumptions. Following the method of moments, we tackle a coupled system of low-rank tensor decomposition problems. The steep costs associated with high-dimensional tensors are avoided, through the development of specialized tensor-free operations. Numerical experiments illustrate the performance of the algorithm and its applicability to various models and applications. In many cases the results exhibit improved reliability over the expectation-maximization algorithm, with similar time and storage costs. We also provide some supporting theory, establishing identifiability and local linear convergence.
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