# Improving Nonparametric Density Estimation with Tensor Decompositions

arXiv: https://arxiv.org/abs/2010.02425 · HTML: https://mlsanity.com/paper/2010.02425/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2020.

## Built on by (most cited first, 4 of 4)

- [Beyond Smoothness: Incorporating Low-Rank Analysis into Nonparametric Density Estimation](https://mlsanity.com/paper/2204.00930/) (2022)
- [Sample Complexity Using Infinite Multiview Models](https://mlsanity.com/paper/2302.04292/) (2023)
- [Generalized Identifiability Bounds for Mixture Models with Grouped Samples](https://mlsanity.com/paper/2207.11164/) (2022)
- [Generalization Bounds for Inductive Matrix Completion in Low-noise Settings](https://mlsanity.com/paper/2212.08339/) (2022)

## Abstract (arXiv)

While nonparametric density estimators often perform well on low dimensional data, their performance can suffer when applied to higher dimensional data, owing presumably to the curse of dimensionality. One technique for avoiding this is to assume no dependence between features and that the data are sampled from a separable density. This allows one to estimate each marginal distribution independently thereby avoiding the slow rates associated with estimating the full joint density. This is a strategy employed in naive Bayes models and is analogous to estimating a rank-one tensor. In this paper we investigate whether these improvements can be extended to other simplified dependence assumptions which we model via nonnegative tensor decompositions. In our central theoretical results we prove that restricting estimation to low-rank nonnegative PARAFAC or Tucker decompositions removes the dimensionality exponent on bin width rates for multidimensional histograms. These results are validated experimentally with high statistical significance via direct application of existing nonnegative tensor factorization to histogram estimators.