Mixtures of product densities are identifiable under a dimension-weighted ell-independence condition, and their nonparametric estimation rate is near-minimax with sample size polynomial in dimension.
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Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models
Mixtures of product densities are identifiable under a dimension-weighted ell-independence condition, and their nonparametric estimation rate is near-minimax with sample size polynomial in dimension.