mlsanityData to 7 Oct 2026

Lower Bounds on the Total Variation Distance Between Mixtures of Two Gaussians

arXiv 2109.01064 ↗First posted 2 Sep 2021math.PR cs.IT cs.LGcited by 4

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Abstract (arXiv)

Mixtures of high dimensional Gaussian distributions have been studied extensively in statistics and learning theory. While the total variation distance appears naturally in the sample complexity of distribution learning, it is analytically difficult to obtain tight lower bounds for mixtures. Exploiting a connection between total variation distance and the characteristic function of the mixture, we provide fairly tight functional approximations. This enables us to derive new lower bounds on the total variation distance between pairs of two-component Gaussian mixtures that have a shared covariance matrix.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 11 of its 35 references that are in the map. First posted on arXiv 2 Sep 2021.

Builds on

11 of 35 references.

References · 11

  1. 2017Mixture Models, Robustness, and Sum of Squares Proofscited by 81
  2. 2019Private Hypothesis Selectioncited by 60
  3. 2016Ten Steps of EM Suffice for Mixtures of Two Gaussianscited by 40
  4. 2014Tight bounds for learning a mixture of two gaussianscited by 29
  5. 2019Private Identity Testing for High-Dimensional Distributionscited by 15
  6. 2020Robust Learning of Mixtures of Gaussianscited by 15
  7. 2019Optimal Average-Case Reductions to Sparse PCA: From Weak Assumptions to Strong Hardnesscited by 13
  8. 2013A Two-round Variant of EM for Gaussian Mixturescited by 11
  9. 2019Learning Distributions Generated by One-Layer ReLU Networkscited by 10
  10. 2020Uniform Convergence Rates for Maximum Likelihood Estimation under Two-Component Gaussian Mixture Modelscited by 6
  11. 2020Algebraic and Analytic Approaches for Parameter Learning in Mixture Modelscited by 4

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Citing papers per year: 2022: 2; 2023: 0; 2024: 1; 2025: 1.

4 papers.

  1. 2024Discriminative Estimation of Total Variation Distance: A Fidelity Auditor for Generative Datacited by 10
  2. 2022Optimal Estimation and Computational Limit of Low-rank Gaussian Mixturescited by 6
  3. 2022Lower Bounds for the Total Variation Distance Given Means and Variances of Distributionscited by 3
  4. 2025Approximating the Total Variation Distance between Gaussianscited by 1