Robust Inference of Dynamic Covariance Using Wishart Processes and Sequential Monte Carlo

TL;DR

This paper introduces a Sequential Monte Carlo method for robustly inferring dynamic covariance matrices using Wishart processes, outperforming traditional methods in accuracy and applicability across disciplines.

Contribution

The paper develops a novel SMC sampler for Wishart processes, providing a more robust inference method compared to MCMC and variational inference.

Findings

SMC yields more robust covariance estimates

SMC outperforms MCMC and variational inference in simulations

Application to clinical depression data demonstrates practical utility

Abstract

Several disciplines, such as econometrics, neuroscience, and computational psychology, study the dynamic interactions between variables over time. A Bayesian nonparametric model known as the Wishart process has been shown to be effective in this situation, but its inference remains highly challenging. In this work, we introduce a Sequential Monte Carlo (SMC) sampler for the Wishart process, and show how it compares to conventional inference approaches, namely MCMC and variational inference. Using simulations we show that SMC sampling results in the most robust estimates and out-of-sample predictions of dynamic covariance. SMC especially outperforms the alternative approaches when using composite covariance functions with correlated parameters. We demonstrate the practical applicability of our proposed approach on a dataset of clinical depression (n=1), and show how using an accurate representation of the posterior distribution can be used to test for dynamics on covariance