Lassoing Eigenvalues

TL;DR

This paper introduces a novel non-smooth penalty method called 'elasso' for sample covariance matrices, which encourages eigenvalue grouping and impacts their estimation properties.

Contribution

The paper proposes a new non-smooth penalty function for covariance matrices, leading to eigenvalue grouping, a novel approach in penalized covariance estimation.

Findings

Eigenvalues are grouped through the elasso method.

The penalty function influences the eigenvalue estimation.

The approach offers a new perspective on covariance matrix regularization.

Abstract

The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of non-smooth penalty functions for the sample covariance matrix, and demonstrate how this method results in a grouping of the estimated eigenvalues. We refer to this method as "lassoing eigenvalues" or as the "elasso".