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[2602.13871] Ensemble-Conditional Gaussian Processes (Ens-CGP): Representation, Geometry, and Inference
Summary
The paper presents Ensemble-Conditional Gaussian Processes (Ens-CGP), linking ensemble inference with conditional Gaussian laws, enhancing understanding of probabilistic models and their computational implementations.
Why It Matters
This research contributes to the field of statistics and machine learning by providing a framework that clarifies the relationship between ensemble methods and Gaussian processes. It has implications for improving inference techniques in various applications, including Kalman filtering and regression analysis.
Key Takeaways
- Introduces Ensemble-Conditional Gaussian Processes (Ens-CGP) for better inference.
- Links probabilistic foundations to ensemble-derived priors.
- Clarifies relationships among probabilistic, variational, and ensemble perspectives.
- Enhances understanding of Kalman filtering and its applications.
- Provides a framework for separating representation from computation.
Mathematics > Statistics Theory arXiv:2602.13871 (math) [Submitted on 14 Feb 2026] 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 View a PDF of the paper titled Ensemble-Conditional Gaussian Processes (Ens-CGP): Representation, Geometry, and Inference, by Sai Ravela and 6 other authors View PDF HTML (experimental) 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 pri...
