Robust Inference of Dynamic Covariance Using Wishart Processes and Sequential Monte Carlo
arxiv(2024)
摘要
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
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