mlsanityData to 7 Oct 2026

Uniform Consistency in Nonparametric Mixture Models

arXiv 2108.14003 ↗First posted 31 Aug 2021math.ST stat.ML stat.THcited by 5

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Abstract (arXiv)

We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error distributions are assumed to be convolutions of a Gaussian density. We construct uniformly consistent estimators under general conditions while simultaneously highlighting several pain points in extending existing pointwise consistency results to uniform results. The resulting analysis turns out to be nontrivial, and several novel technical tools are developed along the way. In the case of mixed regression, we prove L1 convergence of the regression functions while allowing for the component regression functions to intersect arbitrarily often, which presents additional technical challenges. We also consider generalizations to general (i.e. non-convolutional) nonparametric mixtures.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 16 of its 103 references that are in the map. First posted on arXiv 31 Aug 2021.

Builds on

16 of 103 references.

References · 16

  1. 2014Statistical guarantees for the EM algorithm: From population to sample-based analysiscited by 131
  2. 2021Learning latent causal graphs via mixture oraclescited by 55
  3. 2019Convergence Rates for Gaussian Mixtures of Expertscited by 39
  4. 2018Learning Mixtures of Linear Regressions with Nearly Optimal Complexitycited by 37
  5. 2017On Learning Mixtures of Well-Separated Gaussianscited by 30
  6. 2019EM Converges for a Mixture of Many Linear Regressionscited by 27
  7. 2020On the Minimax Optimality of the EM Algorithm for Learning Two-Component Mixed Linear Regressioncited by 24
  8. 2017On the nonparametric maximum likelihood estimator for Gaussian location mixture densities with application to Gaussian denoisingcited by 19
  9. 2016A Universal Approximation Theorem for Mixture of Experts Modelscited by 17
  10. 2018Identifiability of Nonparametric Mixture Models and Bayes Optimal Clusteringcited by 15
  11. 2018Breaking the gridlock in Mixture-of-Experts: Consistent and Efficient Algorithmscited by 13
  12. 2019Deep Divergence-Based Approach to Clusteringcited by 13
4 more
  1. 2016Singularity structures and impacts on parameter estimation in finite mixtures of distributionscited by 9
  2. 2014Nonparametric modal regressioncited by 8
  3. 2020Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observationscited by 8
  4. 2018A convex program for bilinear inversion of sparse vectorscited by 1

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Cited by year

Citing papers per year: 2022: 2; 2023: 1; 2024: 1; 2025: 1.

5 papers.

  1. 2022Tight Bounds on the Hardness of Learning Simple Nonparametric Mixturescited by 3
  2. 2023Sample Complexity Using Infinite Multiview Modelscited by 3
  3. 2022Generalized Identifiability Bounds for Mixture Models with Grouped Samplescited by 2
  4. 2025PMODE: Theoretically Grounded and Modular Mixture Modelingcited by 1
  5. 2024Model-free Estimation of Latent Structure via Multiscale Nonparametric Maximum Likelihoodcited by 0