mlsanityData to 14 Oct 2026

Sample Complexity Using Infinite Multiview Models

arXiv 2302.04292 ↗First posted 8 Feb 2023math.ST stat.ML stat.THcited by 3

Not on the map. Why?

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.

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

14 of 40 references.

References · 14

  1. 2021Low-Rank Sinkhorn Factorizationcited by 67
  2. 2021Tensor-Train Density Estimationcited by 30
  3. 2022Low-rank Optimal Transport: Approximation, Statistics and Debiasingcited by 21
  4. 2018Identifiability of Nonparametric Mixture Models and Bayes Optimal Clusteringcited by 15
  5. 2020Low-rank Characteristic Tensor Density Estimation Part I: Foundationscited by 15
  6. 2019Learning Mixtures of Smooth Product Distributions: Identifiability and Algorithmcited by 14
  7. 2020Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observationscited by 8
  8. 2022Beyond Smoothness: Incorporating Low-Rank Analysis into Nonparametric Density Estimationcited by 8
  9. 2013Nonparametric Estimation of Multi-View Latent Variable Modelscited by 7
  10. 2021Uniform Consistency in Nonparametric Mixture Modelscited by 5
  11. 2020Improving Nonparametric Density Estimation with Tensor Decompositionscited by 4
  12. 2015On The Identifiability of Mixture Models from Grouped Samplescited by 3
2 more
  1. 2022Tight Bounds on the Hardness of Learning Simple Nonparametric Mixturescited by 3
  2. 2022Generalized Identifiability Bounds for Mixture Models with Grouped Samplescited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 1.

3 papers.

  1. 2024Breaking the curse of dimensionality in structured density estimationcited by 3
  2. 2025PMODE: Theoretically Grounded and Modular Mixture Modelingcited by 1
  3. 2026The Silhouette Operator: Identifiability of Low-Rank Measures from One-Dimensional Projectionscited by 0