mlsanityData to 14 Oct 2026

High-dimensional Linear Discriminant Analysis: Optimality, Adaptive Algorithm, and Missing Data

arXiv 1804.03018 ↗First posted 9 Apr 2018stat.MEcited by 17

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Abstract (arXiv)

This paper aims to develop an optimality theory for linear discriminant analysis in the high-dimensional setting. A data-driven and tuning free classification rule, which is based on an adaptive constrained ℓ1 minimization approach, is proposed and analyzed. Minimax lower bounds are obtained and this classification rule is shown to be simultaneously rate optimal over a collection of parameter spaces. In addition, we consider classification with incomplete data under the missing completely at random (MCR) model. An adaptive classifier with theoretical guarantees is introduced and optimal rate of convergence for high-dimensional linear discriminant analysis under the MCR model is established. The technical analysis for the case of missing data is much more challenging than that for the complete data. We establish a large deviation result for the generalized sample covariance matrix, which serves as a key technical tool and can be of independent interest. An application to lung cancer and leukemia studies is also discussed.

Key facts. Cited by 17 papers in the map (data through 14 Oct 2026). First posted on arXiv 9 Apr 2018.

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Citing papers per year: 2021: 2; 2022: 6; 2023: 5; 2024: 1; 2025: 2; 2026: 1.

17 papers.

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  1. 2022Improving Out-of-Distribution Robustness via Selective Augmentationcited by 202
  2. 2023Discover and Cure: Concept-aware Mitigation of Spurious Correlationcited by 71
  3. 2023HappyMap: A Generalized Multi-calibration Methodcited by 18
  4. 2024Learning Invariant Representations of Graph Neural Networks via Cluster Generalizationcited by 10
  5. 2021Minimax Supervised Clustering in the Anisotropic Gaussian Mixture Model: A new take on Robust Interpolationcited by 6
  6. 2022Deep Neural Network Classifier for Multi-dimensional Functional Datacited by 5
  7. 2022Unlabeled Data Help: Minimax Analysis and Adversarial Robustnesscited by 4
  8. 2025Deep learning with missing datacited by 3
  9. 2022Optimal Discriminant Analysis in High-Dimensional Latent Factor Modelscited by 2
  10. 2023Sharp-SSL: Selective high-dimensional axis-aligned random projections for semi-supervised learningcited by 2
  11. 2023Multiclass classification for multidimensional functional data through deep neural networkscited by 1
  12. 2026High-Dimensional Gaussian Mean Estimation under Realizable Contaminationcited by 1
5 more
  1. 2021Classification of high-dimensional data with spiked covariance matrix structurecited by 0
  2. 2022Varying Coefficient Linear Discriminant Analysis for Dynamic Datacited by 0
  3. 2022Interpolating Discriminant Functions in High-Dimensional Gaussian Latent Mixturescited by 0
  4. 2023Pivotal Estimation of Linear Discriminant Analysis in High Dimensionscited by 0
  5. 2025GradMix: Gradient-based Selective Mixup for Robust Data Augmentation in Class-Incremental Learningcited by 0