# Likelihood Geometry of Correlation Models

arXiv: https://arxiv.org/abs/2012.03903 · HTML: https://mlsanity.com/paper/2012.03903/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2020.

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

- [Entropic covariance models](https://mlsanity.com/paper/2306.03590/) (2023)

## Abstract (arXiv)

Correlation matrices are standardized covariance matrices. They form an affine space of symmetric matrices defined by setting the diagonal entries to one. We study the geometry of maximum likelihood estimation for this model and linear submodels that encode additional symmetries. We also consider the problem of minimizing two closely related functions of the covariance matrix: the Stein's loss and the symmetrized Stein's loss. Unlike the Gaussian log-likelihood these two functions are convex and hence admit a unique positive definite optimum. Some of our results hold for general affine covariance models.