# Cross-validation based Nonlinear Shrinkage

arXiv: https://arxiv.org/abs/1611.00798 · HTML: https://mlsanity.com/paper/1611.00798/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2016.

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

- [Holdout cross-validation for large non-Gaussian covariance matrix estimation using Weingarten calculus](https://mlsanity.com/paper/2509.13923/) (2025)
- [How Bregman Divergences Shape Shampoo](https://mlsanity.com/paper/2610.08534/) (2026)

## Abstract (arXiv)

Many machine learning algorithms require precise estimates of covariance matrices. The sample covariance matrix performs poorly in high-dimensional settings, which has stimulated the development of alternative methods, the majority based on factor models and shrinkage. Recent work of Ledoit and Wolf has extended the shrinkage framework to Nonlinear Shrinkage (NLS), a more powerful covariance estimator based on Random Matrix Theory. Our contribution shows that, contrary to claims in the literature, cross-validation based covariance matrix estimation (CVC) yields comparable performance at strongly reduced complexity and runtime. On two real world data sets, we show that the CVC estimator yields superior results than competing shrinkage and factor based methods.