# Entropic covariance models

arXiv: https://arxiv.org/abs/2306.03590 · HTML: https://mlsanity.com/paper/2306.03590/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 97 references that are in the map.
- First posted on arXiv 6 Jun 2023.

## Builds on (most cited first, 9 of 9)

- [Mean estimation and regression under heavy-tailed distributions--a survey](https://mlsanity.com/paper/1906.04280/) (2019)
- [Estimation of High-Dimensional Graphical Models Using Regularized Score Matching](https://mlsanity.com/paper/1507.00433/) (2015)
- [A New Parametrization of Correlation Matrices](https://mlsanity.com/paper/2012.02395/) (2020)
- [Bayesian inference for a covariance matrix](https://mlsanity.com/paper/1408.4050/) (2014)
- [Covariance Prediction via Convex Optimization](https://mlsanity.com/paper/2101.12416/) (2021)
- [Locally associated graphical models and mixed convex exponential families](https://mlsanity.com/paper/2008.04688/) (2020)
- [Stochastic Chebyshev Gradient Descent for Spectral Optimization](https://mlsanity.com/paper/1802.06355/) (2018)
- [Gibbs Manifolds](https://mlsanity.com/paper/2211.15490/) (2022)
- [Likelihood Geometry of Correlation Models](https://mlsanity.com/paper/2012.03903/) (2020)

## Abstract (arXiv)

In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance matrix or its inverse. Another approach considers linear restrictions on the matrix logarithm of the covariance matrix. In this paper, we present a general framework for linear restrictions on different transformations of the covariance matrix, including the mentioned examples. Our proposed estimation method solves a convex problem and yields an M-estimator, allowing for relatively straightforward asymptotic (in general) and finite sample analysis (in the Gaussian case). In particular, we recover standard √n/d rates, where d is the dimension of the underlying model. Our geometric insights allow to extend various recent results in covariance matrix modelling. This includes providing unrestricted parametrizations of the space of correlation matrices, which is alternative to a recent result utilizing the matrix logarithm.