# Large dimensional analysis of general margin based classification methods

arXiv: https://arxiv.org/abs/1901.08057 · HTML: https://mlsanity.com/paper/1901.08057/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2019.

## Built on by (most cited first, 3 of 3)

- [The Breakdown of Gaussian Universality in Classification of High-dimensional Linear Factor Mixtures](https://mlsanity.com/paper/2410.05609/) (2024)
- [Statistical Inference in Classification of High-dimensional Gaussian Mixture](https://mlsanity.com/paper/2410.19950/) (2024)
- [Hadamard-Riemannian Optimization for Margin-Variance Ensemble](https://mlsanity.com/paper/2509.10189/) (2025)

## Abstract (arXiv)

Margin-based classifiers have been popular in both machine learning and statistics for classification problems. Since a large number of classifiers are available, one natural question is which type of classifiers should be used given a particular classification task. We answer this question by investigating the asymptotic performance of a family of large-margin classifiers under the two component mixture models in situations where the data dimension p and the sample n are both large. This family covers a broad range of classifiers including support vector machine, distance weighted discrimination, penalized logistic regression, and large-margin unified machine as special cases. The asymptotic results are described by a set of nonlinear equations and we observe a close match of them with Monte Carlo simulation on finite data samples. Our analytical studies shed new light on how to select the best classifier among various classification methods as well as on how to choose the optimal tuning parameters for a given method.