Gaussian Ensemble Belief Propagation for Efficient Inference in High-Dimensional, Black-box Systems

Dan MacKinlay, Russell Tsuchida, Daniel Edward Pagendam, Petra Kuhnert

Keywords: factor graph, data assimilation, ensemble kalman filter, gaussian belief propagation, geospatial, probabilistic graphical model, hierarchical model

TL;DR: If we carefully combine the structures of the Ensemble Kalman Gfilter and Gaussian Belief Propagation, the result is an efficient method for inference in hierarchical spatial systems

Abstract:

Efficient inference in high-dimensional models is a central challenge in machine learning.
We introduce the Gaussian Ensemble Belief Propagation (GEnBP) algorithm, which combines the strengths of the Ensemble Kalman Filter (EnKF) and Gaussian Belief Propagation (GaBP) to address this challenge.
GEnBP updates ensembles of prior samples into posterior samples by passing low-rank local messages over the edges of a graphical model, enabling efficient handling of high-dimensional states, parameters, and complex, noisy, black-box generative processes.
By utilizing local message passing within a graphical model structure, GEnBP effectively manages complex dependency structures and remains computationally efficient even when the ensemble size is much smaller than the inference dimension --- a common scenario in spatiotemporal modeling, image processing, and physical model inversion.
We demonstrate that GEnBP can be applied to various problem structures, including data assimilation, system identification, and hierarchical models, and show through experiments that it outperforms existing belief propagation methods in terms of accuracy and computational efficiency.

Supporting code is available at https://github.com/danmackinlay/GEnBP}{github.com/danmackinlay/GEnBP

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 5238