# Statistical Inference in Classification of High-dimensional Gaussian Mixture

arXiv: https://arxiv.org/abs/2410.19950 · HTML: https://mlsanity.com/paper/2410.19950/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 50 references that are in the map.
- First posted on arXiv 25 Oct 2024.

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

- [High-Dimensional Asymptotics of Prediction: Ridge Regression and Classification](https://mlsanity.com/paper/1507.03003/) (2015)
- [Generalisation error in learning with random features and the hidden manifold model](https://mlsanity.com/paper/2002.09339/) (2020)
- [Learning curves of generic features maps for realistic datasets with a teacher-student model](https://mlsanity.com/paper/2102.08127/) (2021)
- [A Model of Double Descent for High-dimensional Binary Linear Classification](https://mlsanity.com/paper/1911.05822/) (2019)
- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [The role of regularization in classification of high-dimensional noisy Gaussian mixture](https://mlsanity.com/paper/2002.11544/) (2020)
- [Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensions](https://mlsanity.com/paper/2106.03791/) (2021)
- [The phase transition for the existence of the maximum likelihood estimate in high-dimensional logistic regression](https://mlsanity.com/paper/1804.09753/) (2018)
- [Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (or : How to Prove Kabashima's Replica Formula)](https://mlsanity.com/paper/2006.06581/) (2020)
- [Hypothesis Testing in High-Dimensional Regression under the Gaussian Random Design Model: Asymptotic Theory](https://mlsanity.com/paper/1301.4240/) (2013)
- [Distributed Inference for Linear Support Vector Machine](https://mlsanity.com/paper/1811.11922/) (2018)
- [A statistical mechanics approach to de-biasing and uncertainty estimation in LASSO for random measurements](https://mlsanity.com/paper/1803.09927/) (2018)
- [Large dimensional analysis of general margin based classification methods](https://mlsanity.com/paper/1901.08057/) (2019)
- [Compressed sensing radar detectors under the row-orthogonal design model: a statistical mechanics perspective](https://mlsanity.com/paper/2209.15273/) (2022)

## Abstract (arXiv)

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of regularized convex classifiers in the high-dimensional limit, where both the sample size n and the dimension p approach infinity while their ratio α=n/p remains fixed. Our focus is on the generalization error and variable selection properties of the estimators. Specifically, based on the distributional limit of the classifier, we construct a de-biased estimator to perform variable selection through an appropriate hypothesis testing procedure. Using L1-regularized logistic regression as an example, we conducted extensive computational experiments to confirm that our analytical findings are consistent with numerical simulations in finite-sized systems. We also explore the influence of the covariance structure on the performance of the de-biased estimator.