Support Recovery in Mixture Models With Sparse Parameters

Mixture models are widely used to fit complex and multimodal datasets. In this paper we study mixtures with high dimensional sparse parameter vectors and consider the problem of support recovery of those vectors. While parameter learning in mixture models is well-studied, the sparsity constraint remains relatively unexplored. Sparsity of parameter vectors is a natural assumption in high dimensional settings, and support recovery is a major step towards parameter estimation. We provide efficient algorithms for support recovery that have a logarithmic sample complexity dependence on the dimensionality of the latent space, and also poly-logarithmic dependence on sparsity. Our algorithms, applicable to mixtures of many different canonical distributions including high dimensional Uniform, Poisson, Laplace, Gaussians, etc., are based on the method of moments. In most of these settings, our results are the first guarantees on the problem while in the rest, our results provide improvements on or are competitive with existing works.