# Optimal Discriminant Analysis in High-Dimensional Latent Factor Models

arXiv: https://arxiv.org/abs/2210.12862 · HTML: https://mlsanity.com/paper/2210.12862/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 57 references that are in the map.
- First posted on arXiv 23 Oct 2022.

## Builds on (most cited first, 7 of 7)

- [Adaptive Estimation in Structured Factor Models with Applications to Overlapping Clustering](https://mlsanity.com/paper/1704.06977/) (2017)
- [High-dimensional Linear Discriminant Analysis: Optimality, Adaptive Algorithm, and Missing Data](https://mlsanity.com/paper/1804.03018/) (2018)
- [Sufficient Forecasting Using Factor Models](https://mlsanity.com/paper/1505.07414/) (2015)
- [Minimax Theory for High-dimensional Gaussian Mixtures with Sparse Mean Separation](https://mlsanity.com/paper/1306.2035/) (2013)
- [A Convex Optimization Approach to High-Dimensional Sparse Quadratic Discriminant Analysis](https://mlsanity.com/paper/1912.02872/) (2019)
- [Multiclass Sparse Discriminant Analysis](https://mlsanity.com/paper/1504.05845/) (2015)
- [Adaptive estimation of the rank of the coefficient matrix in high dimensional multivariate response regression models](https://mlsanity.com/paper/1704.02381/) (2017)

## Built on by (most cited first, 2 of 2)

- [Interpolating Discriminant Functions in High-Dimensional Gaussian Latent Mixtures](https://mlsanity.com/paper/2210.14347/) (2022)
- [Inference with non-differentiable surrogate loss in a general high-dimensional classification framework](https://mlsanity.com/paper/2405.11723/) (2024)

## Abstract (arXiv)

In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this paper, we formulate a latent-variable model with a hidden low-dimensional structure to justify this two-step procedure and to guide which projection to choose. We propose a computationally efficient classifier that takes certain principal components (PCs) of the observed features as projections, with the number of retained PCs selected in a data-driven way. A general theory is established for analyzing such two-step classifiers based on any projections. We derive explicit rates of convergence of the excess risk of the proposed PC-based classifier. The obtained rates are further shown to be optimal up to logarithmic factors in the minimax sense. Our theory allows the lower-dimension to grow with the sample size and is also valid even when the feature dimension (greatly) exceeds the sample size. Extensive simulations corroborate our theoretical findings. The proposed method also performs favorably relative to other existing discriminant methods on three real data examples.