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 generation 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 methods in terms of accuracy and computational efficiency. Supporting code is available at https://github.com/danmackinlay/GEnBP

翻译：高效推理高维模型是机器学习的核心挑战。本文提出高斯集成置信传播算法，该算法融合了集成卡尔曼滤波器与高斯置信传播的优势以应对这一挑战。GEnBP通过在图模型的边上传递低秩局部信息，将先验样本集更新为后验样本，从而能够高效处理高维状态、参数以及复杂、含噪声的黑箱生成过程。通过在图模型结构内部利用局部信息传递机制，GEnBP能有效管理复杂的依赖结构，即使在集成规模远小于推理维度的常见场景（如时空建模、图像处理和物理模型反演）中仍保持计算高效性。我们证明GEnBP可适用于多种问题结构，包括数据同化、系统辨识和层次模型，并通过实验表明其在精度与计算效率方面均优于现有方法。相关代码已发布于 https://github.com/danmackinlay/GEnBP