# Eigengap Sparsity for Covariance Parsimony

arXiv: https://arxiv.org/abs/2504.10110 · HTML: https://mlsanity.com/paper/2504.10110/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2025.

## Built on by (most cited first, 1 of 1)

- [Parsimonious Gaussian mixture models with piecewise-constant eigenvalue profiles](https://mlsanity.com/paper/2507.01542/) (2025)

## Abstract (arXiv)

Covariance estimation is a central problem in statistics. An important issue is that there are rarely enough samples n to accurately estimate the p (p+1) / 2 coefficients in dimension p. Parsimonious covariance models are therefore preferred, but the discrete nature of model selection makes inference computationally challenging. In this paper, we propose a relaxation of covariance parsimony termed "eigengap sparsity" and motivated by the good accuracy-parsimony tradeoffs of eigenvalue-equalization in covariance matrices. This penalty can be included in a penalized-likelihood framework that we propose to solve with a projected gradient descent on a monotone cone. The algorithm turns out to resemble an isotonic regression of mutually-attracted sample eigenvalues, drawing an interesting link between covariance parsimony and shrinkage.