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The construction and theoretical analysis of the most popular universallyconsistent nonparametric density estimators hinge on one functional property:smoothness. In this paper we investigate the theoretical implications ofincorporating a multi-view latent variable model, a type of low-rank model,into nonparametric density estimation. To do this we perform extensive analysison histogram-style estimators that integrate a multi-view model. Our analysisculminates in showing that there exists a universally consistenthistogram-style estimator that converges to any multi-view model with a finitenumber of Lipschitz continuous components at a rate of$\widetilde{O}(1/\sqrt[3]{n})$ in $L^1$ error. In contrast, the standardhistogram estimator can converge at a rate slower than $1/\sqrt[d]{n}$ on thesame class of densities. We also introduce a new nonparametric latent variablemodel based on the Tucker decomposition. A rudimentary implementation of ourestimators experimentally demonstrates a considerable performance improvementover the standard histogram estimator. We also provide a thorough analysis ofthe sample complexity of our Tucker decomposition-based model and a variety ofother results. Thus, our paper provides solid theoretical foundations forextending low-rank techniques to the nonparametric setting

Beyond Smoothness: Incorporating Low-Rank Analysis into Nonparametric Density Estimation