Cleaning the correlation matrix with a denoising autoencoder

TL;DR

This paper introduces an adjusted autoencoder to improve estimation of true eigenvalues of correlation matrices from limited samples, outperforming existing estimators in high-dimensional settings.

Contribution

The paper proposes a novel autoencoder-based method for denoising correlation matrices, demonstrating superior performance over the Rotational Invariant Estimator in small-sample, high-dimensional scenarios.

Findings

Autoencoder effectively estimates true eigenvalues from sample data.

Outperforms the Rotational Invariant Estimator in simulations.

Provides a new approach for correlation matrix denoising in high-dimensional statistics.

Abstract

In this paper, we use an adjusted autoencoder to estimate the true eigenvalues of the population correlation matrix from the sample correlation matrix when the number of samples is small. We show that the model outperforms the Rotational Invariant Estimator (Bouchaud) which is the optimal estimator in the sample eigenvectors basis when the dimension goes to infinity.