WeSpeR: Computing non-linear shrinkage formulas for the weighted sample covariance

TL;DR

This paper introduces the WeSpeR algorithm, which efficiently computes non-linear shrinkage formulas for weighted sample covariance matrices in high-dimensional settings, significantly improving speed and accuracy.

Contribution

The paper develops a novel algorithm, WeSpeR, leveraging asymptotic spectral properties to accelerate non-linear shrinkage computations for high-dimensional weighted covariance matrices.

Findings

WeSpeR significantly speeds up non-linear shrinkage in dimensions over 1000.

Empirical tests show WeSpeR has good accuracy and stability.

Implementation available in PyTorch for practical use.

Abstract

We address the issue of computing the non-linear shrinkage formulas for the weighted sample covariance in high dimension. We use theoretical properties of the asymptotic sample spectrum in order to derive the \textit{WeSpeR} algorithm and significantly speed up non-linear shrinkage in dimension higher than $1000$. Empirical tests confirm the good properties of the \textit{WeSpeR} algorithm. We provide the implementation in PyTorch for it.