Efficient inference in high-dimensional models remains a central challenge in machine learning. This paper introduces the Gaussian Ensemble Belief Propagation (GEnBP) algorithm, a fusion of the Ensemble Kalman filter and Gaussian belief propagation (GaBP) methods. GEnBP updates ensembles by passing low-rank local messages in a graphical model structure. This combination inherits favourable qualities from each method. Ensemble techniques allow GEnBP to handle high-dimensional states, parameters and intricate, noisy, black-box generation processes. The use of local messages in a graphical model structure ensures that the approach is suited to distributed computing and can efficiently handle complex dependence structures. GEnBP is particularly advantageous when the ensemble size is considerably smaller than the inference dimension. This scenario often arises in fields such as spatiotemporal modelling, image processing and physical model inversion. GEnBP can be applied to general problem structures, including jointly learning system parameters, observation parameters, and latent state variables.

翻译：高维模型的高效推理仍是机器学习领域的核心挑战。本文提出高斯集成信念传播（GEnBP）算法，该算法融合了集成卡尔曼滤波与高斯信念传播方法。GEnBP通过在图形模型结构中传递低秩局部消息来更新集成。这种结合继承了两种方法的优良特性：集成技术使GEnBP能够处理高维状态、参数以及复杂含噪的黑箱生成过程；图形模型结构中的局部消息则确保该方法适用于分布式计算，并能高效处理复杂依赖结构。当集成规模远小于推理维度时，GEnBP优势尤为显著。这一场景常见于时空建模、图像处理和物理模型反演等领域。GEnBP可应用于通用问题结构，包括系统参数、观测参数与隐状态变量的联合学习。