Ensemble-Conditional Gaussian Processes (Ens-CGP): Representation, Geometry, and Inference
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918339504242688 |
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| author | Ravela, Sai Kim, Jae Deok Gee, Kenneth Yan, Xingjian Mercier, Samson Albarghouty, Lubna Saha, Anamitra |
| author_facet | Ravela, Sai Kim, Jae Deok Gee, Kenneth Yan, Xingjian Mercier, Samson Albarghouty, Lubna Saha, Anamitra |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_13871 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ensemble-Conditional Gaussian Processes (Ens-CGP): Representation, Geometry, and Inference Ravela, Sai Kim, Jae Deok Gee, Kenneth Yan, Xingjian Mercier, Samson Albarghouty, Lubna Saha, Anamitra Statistics Theory Information Theory Machine Learning Optimization and Control Applications 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. |
| title | Ensemble-Conditional Gaussian Processes (Ens-CGP): Representation, Geometry, and Inference |
| topic | Statistics Theory Information Theory Machine Learning Optimization and Control Applications |
| url | https://arxiv.org/abs/2602.13871 |