Reproduce “Ensemble-Conditional Gaussian Processes (Ens-CGP): Representation, Geometry, and Inference” on OpenResearch

About this paper

Sai Ravela, Jae Deok Kim, Kenneth Gee, Xingjian Yan, Samson Mercier, Lubna Albarghouty, Anamitra Saha

This research unifies diverse statistical inference fields—Gaussian processes, kernel methods, quadratic optimization, and Kalman filters—under a single finite-dimensional framework, introducing Ensemble-Conditional Gaussian Processes (Ens-CGP). It formally proves their mathematical equivalence in linear-Gaussian settings and clarifies the probabilistic role of ensembles in defining low-rank Gaussian priors for robust inference.

Key insights

• Diverse inference methodologies like Gaussian Processes, RKHS regression, quadratic optimization, and Kalman filter analysis are mathematically equivalent in finite-dimensional linear-Gaussian settings.
• Ensembles can be explicitly defined as instantiating a (potentially low-rank) Gaussian prior, providing a clearer probabilistic foundation for ensemble-based methods.
• Repeatedly treating the same observation as independent information in sequential Bayesian updates leads to 'posterior collapse,' causing the posterior covariance to tend to zero.

Summary by alphaXiv.