mlsanityData to 7 Oct 2026

A Novel Gaussian Min-Max Theorem and its Applications

arXiv 2402.07356 ↗First posted 12 Feb 2024cs.LG stat.MLcited by 4

Not on the map. Why?

Abstract (arXiv)

A celebrated result by Gordon allows one to compare the min-max behavior of two Gaussian processes if certain inequality conditions are met. The consequences of this result include the Gaussian min-max (GMT) and convex Gaussian min-max (CGMT) theorems which have had far-reaching implications in high-dimensional statistics, machine learning, non-smooth optimization, and signal processing. Both theorems rely on a pair of Gaussian processes, first identified by Slepian, that satisfy Gordon's comparison inequalities. In this paper, we identify such a new pair. The resulting theorems extend the classical GMT and CGMT Theorems from the case where the underlying Gaussian matrix in the primary process has iid rows to where it has independent but non-identically-distributed ones. The new CGMT is applied to the problems of multi-source Gaussian regression, as well as to binary classification of general Gaussian mixture models.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 18 of its 32 references that are in the map. First posted on arXiv 12 Feb 2024.

Builds on

18 of 32 references.

References · 18

  1. 2016CVXPY: A Python-Embedded Modeling Language for Convex Optimizationcited by 633
  2. 2017A Rewriting System for Convex Optimization Problemscited by 178
  3. 2022Universality of empirical risk minimizationcited by 73
  4. 2020The role of regularization in classification of high-dimensional noisy Gaussian mixturecited by 63
  5. 2021Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensionscited by 52
  6. 2020Precise Statistical Analysis of Classification Accuracies for Adversarial Trainingcited by 49
  7. 2013A framework to characterize performance of LASSO algorithmscited by 38
  8. 2019The Impact of Regularization on High-dimensional Logistic Regressioncited by 35
  9. 2020Theoretical Insights Into Multiclass Classification: A High-dimensional Asymptotic Viewcited by 32
  10. 2023Universality laws for Gaussian mixtures in generalized linear modelscited by 28
  11. 2019The generalization error of max-margin linear classifiers: Benign overfitting and high dimensional asymptotics in the overparametrized regimecited by 27
  12. 2024Scaling laws for learning with real and surrogate datacited by 26
6 more
  1. 2021On the Inherent Regularization Effects of Noise Injection During Trainingcited by 18
  2. 2020Sharp Asymptotics and Optimal Performance for Inference in Binary Modelscited by 13
  3. 2020The Performance Analysis of Generalized Margin Maximizer (GMM) on Separable Datacited by 7
  4. 2023Regularized Linear Regression for Binary Classificationcited by 7
  5. 2022Wasserstein Distributionally Robust Estimation in High Dimensions: Performance Analysis and Optimal Hyperparameter Tuningcited by 6
  6. 2023Uniform Convergence with Square-Root Lipschitz Losscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2026Characterization of Gaussian Universality Breakdown in High-Dimensional Empirical Risk Minimizationcited by 1
  2. 2025One-Bit Quantization for Random Features Modelscited by 0
  3. 2026Asymptotic Behavior of Multi--Task Learning: Implicit Regularization and Double Descent Effectscited by 0
  4. 2026Precise Performance of Linear Denoisers in the Proportional Regimecited by 0