# Sample Complexity Using Infinite Multiview Models

arXiv: https://arxiv.org/abs/2302.04292 · HTML: https://mlsanity.com/paper/2302.04292/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 8 Feb 2023.

## Builds on (most cited first, 14 of 14)

- [Low-Rank Sinkhorn Factorization](https://mlsanity.com/paper/2103.04737/) (2021)
- [Tensor-Train Density Estimation](https://mlsanity.com/paper/2108.00089/) (2021)
- [Low-rank Optimal Transport: Approximation, Statistics and Debiasing](https://mlsanity.com/paper/2205.12365/) (2022)
- [Identifiability of Nonparametric Mixture Models and Bayes Optimal Clustering](https://mlsanity.com/paper/1802.04397/) (2018)
- [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)
- [Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observations](https://mlsanity.com/paper/2006.07459/) (2020)
- [Beyond Smoothness: Incorporating Low-Rank Analysis into Nonparametric Density Estimation](https://mlsanity.com/paper/2204.00930/) (2022)
- [Nonparametric Estimation of Multi-View Latent Variable Models](https://mlsanity.com/paper/1311.3287/) (2013)
- [Uniform Consistency in Nonparametric Mixture Models](https://mlsanity.com/paper/2108.14003/) (2021)
- [Improving Nonparametric Density Estimation with Tensor Decompositions](https://mlsanity.com/paper/2010.02425/) (2020)
- [On The Identifiability of Mixture Models from Grouped Samples](https://mlsanity.com/paper/1502.06644/) (2015)
- [Tight Bounds on the Hardness of Learning Simple Nonparametric Mixtures](https://mlsanity.com/paper/2203.15150/) (2022)
- [Generalized Identifiability Bounds for Mixture Models with Grouped Samples](https://mlsanity.com/paper/2207.11164/) (2022)

## Built on by (most cited first, 3 of 3)

- [Breaking the curse of dimensionality in structured density estimation](https://mlsanity.com/paper/2410.07685/) (2024)
- [PMODE: Theoretically Grounded and Modular Mixture Modeling](https://mlsanity.com/paper/2508.21396/) (2025)
- [The Silhouette Operator: Identifiability of Low-Rank Measures from One-Dimensional Projections](https://mlsanity.com/paper/2610.09687/) (2026)

## Abstract (arXiv)

Recent works have demonstrated that the convergence rate of a nonparametric density estimator can be greatly improved by using a low-rank estimator when the target density is a convex combination of separable probability densities with Lipschitz continuous marginals, i.e. a multiview model. However, this assumption is very restrictive and it is not clear to what degree these findings can be extended to general pdfs. This work answers this question by introducing a new way of characterizing a pdf's complexity, the non-negative Lipschitz spectrum (NL-spectrum), which, unlike smoothness properties, can be used to characterize virtually any pdf. Finite sample bounds are presented that are dependent on the target density's NL-spectrum. From this dimension-independent rates of convergence are derived that characterize when an NL-spectrum allows for a fast rate of convergence.