Maximum A Posteriori Covariance Estimation Using a Power Inverse Wishart Prior

TL;DR

This paper introduces a fast, computationally efficient MAP estimator for covariance matrices using a novel class of priors that generalize the inverse Wishart, improving estimation in high-dimensional settings.

Contribution

The paper proposes a new class of prior distributions for covariance estimation, enabling a quick MAP estimator that generalizes the inverse Wishart prior.

Findings

Performs well on simulated data

Demonstrates effectiveness on real data

Offers a computationally efficient alternative

Abstract

The estimation of the covariance matrix is an initial step in many multivariate statistical methods such as principal components analysis and factor analysis, but in many practical applications the dimensionality of the sample space is large compared to the number of samples, and the usual maximum likelihood estimate is poor. Typically, improvements are obtained by modelling or regularization. From a practical point of view, these methods are often computationally heavy and rely on approximations. As a fast substitute, we propose an easily calculable maximum a posteriori (MAP) estimator based on a new class of prior distributions generalizing the inverse Wishart prior, discuss its properties, and demonstrate the estimator on simulated and real data.