Covariance Prediction via Convex Optimization

TL;DR

This paper introduces a convex optimization-based method for predicting the covariance matrix of a Gaussian vector from features, using a generalized linear model structure with positive definite constraints.

Contribution

It proposes a novel covariance predictor model with a convex log-likelihood, enabling efficient fitting and recursive application for improved performance.

Findings

The predictor is formulated as a convex optimization problem.

The model ensures positive definiteness of covariance estimates.

Recursive application enhances prediction accuracy.

Abstract

We consider the problem of predicting the covariance of a zero mean Gaussian vector, based on another feature vector. We describe a covariance predictor that has the form of a generalized linear model, i.e., an affine function of the features followed by an inverse link function that maps vectors to symmetric positive definite matrices. The log-likelihood is a concave function of the predictor parameters, so fitting the predictor involves convex optimization. Such predictors can be combined with others, or recursively applied to improve performance.