Scalable marginalization of correlated latent variables with applications to learning particle interaction kernels

Understand

Marginalization of latent variables or nuisance parameters is a fundamental aspect of Bayesian inference and uncertainty quantification.

• In this work, we focus on scalable marginalization of latent variables in modeling correlated data, such as spatio-temporal or functional observations.
• We first introduce Gaussian processes (GPs) for modeling correlated data and highlight the computational challenge, where the computational complexity increases cubically fast along with the number of observations.
• We then review the connection between the state space model and GPs with Mat{\'e}rn covariance for temporal inputs.