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

arXiv: https://arxiv.org/abs/2204.00930 · HTML: https://mlsanity.com/paper/2204.00930/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 60 references that are in the map.
- First posted on arXiv 2 Apr 2022.

## Builds on (most cited first, 12 of 12)

- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
- [Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations](https://mlsanity.com/paper/1606.01855/) (2016)
- [Tensors, Learning, and 'Kolmogorov Extension' for Finite-alphabet Random Vectors](https://mlsanity.com/paper/1712.00205/) (2017)
- [Low-rank Characteristic Tensor Density Estimation Part I: Foundations](https://mlsanity.com/paper/2008.12315/) (2020)
- [Learning Mixtures of Smooth Product Distributions: Identifiability and Algorithm](https://mlsanity.com/paper/1904.01156/) (2019)
- [Source Identification for Mixtures of Product Distributions](https://mlsanity.com/paper/2012.14540/) (2020)
- [Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observations](https://mlsanity.com/paper/2006.07459/) (2020)
- [Low-rank Characteristic Tensor Density Estimation Part II: Compression and Latent Density Estimation](https://mlsanity.com/paper/2106.10591/) (2021)
- [Recovery Guarantees for Kernel-based Clustering under Non-parametric Mixture Models](https://mlsanity.com/paper/2110.09476/) (2021)
- [Improving Nonparametric Density Estimation with Tensor Decompositions](https://mlsanity.com/paper/2010.02425/) (2020)
- [Robust Kernel Density Estimation by Scaling and Projection in Hilbert Space](https://mlsanity.com/paper/1411.4378/) (2014)
- [Consistent Kernel Density Estimation with Non-Vanishing Bandwidth](https://mlsanity.com/paper/1705.08921/) (2017)

## Built on by (most cited first, 8 of 8)

- [Sample Complexity Using Infinite Multiview Models](https://mlsanity.com/paper/2302.04292/) (2023)
- [Scale adaptive and robust intrinsic dimension estimation via optimal neighbourhood identification](https://mlsanity.com/paper/2405.15132/) (2024)
- [Breaking the curse of dimensionality in structured density estimation](https://mlsanity.com/paper/2410.07685/) (2024)
- [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)
- [PMODE: Theoretically Grounded and Modular Mixture Modeling](https://mlsanity.com/paper/2508.21396/) (2025)
- [Explainable Neural Networks with Guarantees: A Sparse Estimation Approach](https://mlsanity.com/paper/2501.02010/) (2025)
- [Generalization Bounds for Semi-supervised Matrix Completion with Distributional Side Information](https://mlsanity.com/paper/2511.13049/) (2025)

## Abstract (arXiv)

The construction and theoretical analysis of the most popular universally consistent nonparametric density estimators hinge on one functional property: smoothness. In this paper we investigate the theoretical implications of incorporating a multi-view latent variable model, a type of low-rank model, into nonparametric density estimation. To do this we perform extensive analysis on histogram-style estimators that integrate a multi-view model. Our analysis culminates in showing that there exists a universally consistent histogram-style estimator that converges to any multi-view model with a finite number of Lipschitz continuous components at a rate of widetildeO(1/√[3]n) in L1 error. In contrast, the standard histogram estimator can converge at a rate slower than 1/√[d]n on the same class of densities. We also introduce a new nonparametric latent variable model based on the Tucker decomposition. A rudimentary implementation of our estimators experimentally demonstrates a considerable performance improvement over the standard histogram estimator. We also provide a thorough analysis of the sample complexity of our Tucker decomposition-based model and a variety of other results. Thus, our paper provides solid theoretical foundations for extending low-rank techniques to the nonparametric setting