# Interpolating Discriminant Functions in High-Dimensional Gaussian Latent Mixtures

arXiv: https://arxiv.org/abs/2210.14347 · HTML: https://mlsanity.com/paper/2210.14347/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 25 Oct 2022.

## Builds on (most cited first, 12 of 12)

- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Harmless interpolation of noisy data in regression](https://mlsanity.com/paper/1903.09139/) (2019)
- [Overfitting or perfect fitting? Risk bounds for classification and regression rules that interpolate](https://mlsanity.com/paper/1806.05161/) (2018)
- [Finite-sample Analysis of Interpolating Linear Classifiers in the Overparameterized Regime](https://mlsanity.com/paper/2004.12019/) (2020)
- [Risk Bounds for Over-parameterized Maximum Margin Classification on Sub-Gaussian Mixtures](https://mlsanity.com/paper/2104.13628/) (2021)
- [On the proliferation of support vectors in high dimensions](https://mlsanity.com/paper/2009.10670/) (2020)
- [High-dimensional Linear Discriminant Analysis: Optimality, Adaptive Algorithm, and Missing Data](https://mlsanity.com/paper/1804.03018/) (2018)
- [Minimax Supervised Clustering in the Anisotropic Gaussian Mixture Model: A new take on Robust Interpolation](https://mlsanity.com/paper/2111.07041/) (2021)
- [Adaptive estimation of the rank of the coefficient matrix in high dimensional multivariate response regression models](https://mlsanity.com/paper/1704.02381/) (2017)
- [Optimal Discriminant Analysis in High-Dimensional Latent Factor Models](https://mlsanity.com/paper/2210.12862/) (2022)

## Abstract (arXiv)

This paper considers binary classification of high-dimensional features under a postulated model with a low-dimensional latent Gaussian mixture structure and non-vanishing noise. A generalized least squares estimator is used to estimate the direction of the optimal separating hyperplane. The estimated hyperplane is shown to interpolate on the training data. While the direction vector can be consistently estimated as could be expected from recent results in linear regression, a naive plug-in estimate fails to consistently estimate the intercept. A simple correction, that requires an independent hold-out sample, renders the procedure minimax optimal in many scenarios. The interpolation property of the latter procedure can be retained, but surprisingly depends on the way the labels are encoded.