# A Convex Optimization Approach to High-Dimensional Sparse Quadratic Discriminant Analysis

arXiv: https://arxiv.org/abs/1912.02872 · HTML: https://mlsanity.com/paper/1912.02872/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2019.

## Built on by (most cited first, 10 of 10)

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- [Multiclass classification for multidimensional functional data through deep neural networks](https://mlsanity.com/paper/2305.13349/) (2023)
- [Classification of high-dimensional data with spiked covariance matrix structure](https://mlsanity.com/paper/2110.01950/) (2021)
- [Spectrally-Corrected and Regularized QDA Classifier for Spiked Covariance Model](https://mlsanity.com/paper/2503.13582/) (2025)
- [GradMix: Gradient-based Selective Mixup for Robust Data Augmentation in Class-Incremental Learning](https://mlsanity.com/paper/2505.08528/) (2025)
- [Multi-Group Quadratic Discriminant Analysis via Projection](https://mlsanity.com/paper/2601.05415/) (2026)

## Abstract (arXiv)

In this paper, we study high-dimensional sparse Quadratic Discriminant Analysis (QDA) and aim to establish the optimal convergence rates for the classification error. Minimax lower bounds are established to demonstrate the necessity of structural assumptions such as sparsity conditions on the discriminating direction and differential graph for the possible construction of consistent high-dimensional QDA rules. We then propose a classification algorithm called SDAR using constrained convex optimization under the sparsity assumptions. Both minimax upper and lower bounds are obtained and this classification rule is shown to be simultaneously rate optimal over a collection of parameter spaces, up to a logarithmic factor. Simulation studies demonstrate that SDAR performs well numerically. The algorithm is also illustrated through an analysis of prostate cancer data and colon tissue data. The methodology and theory developed for high-dimensional QDA for two groups in the Gaussian setting are also extended to multi-group classification and to classification under the Gaussian copula model.