Ensemble-Conditional Gaussian Processes (Ens-CGP): Representation, Geometry, and Inference

• URL: http://arxiv.org/abs/2602.13871v1
• Date: Sat, 14 Feb 2026 20:00:43 GMT
• Title: Ensemble-Conditional Gaussian Processes (Ens-CGP): Representation, Geometry, and Inference
• Authors: Sai Ravela, Jae Deok Kim, Kenneth Gee, Xingjian Yan, Samson Mercier, Lubna Albarghouty, Anamitra Saha,
• Abstract summary: We formulate Ensemble-Conditional Gaussian Processes (Ens-CGP)<n>Ens-CGP is a finite-dimensional synthesis that centers ensemble-based inference on the conditional Gaussian law.<n>By separating representation (GP -> CGP -> Ens-CGP) from computation, the framework links an earlier-established representational foundation for inference to ensemble-derived priors.
• Score: 1.9319772479956787
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We formulate Ensemble-Conditional Gaussian Processes (Ens-CGP), a finite-dimensional synthesis that centers ensemble-based inference on the conditional Gaussian law. Conditional Gaussian processes (CGP) arise directly from Gaussian processes under conditioning and, in linear-Gaussian settings, define the full posterior distribution for a Gaussian prior and linear observations. Classical Kalman filtering is a recursive algorithm that computes this same conditional law under dynamical assumptions; the conditional Gaussian law itself is therefore the underlying representational object, while the filter is one computational realization. In this sense, CGP provides the probabilistic foundation for Kalman-type methods as well as equivalent formulations as a strictly convex quadratic program (MAP estimation), RKHS-regularized regression, and classical regularization. Ens-CGP is the ensemble instantiation of this object, obtained by treating empirical ensemble moments as a (possibly low-rank) Gaussian prior and performing exact conditioning. By separating representation (GP -> CGP -> Ens-CGP) from computation (Kalman filters, EnKF variants, and iterative ensemble schemes), the framework links an earlier-established representational foundation for inference to ensemble-derived priors and clarifies the relationships among probabilistic, variational, and ensemble perspectives.

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