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：高维模型的高效推断仍是机器学习领域的核心挑战。本文提出高斯集成置信传播算法，融合了集成卡尔曼滤波与高斯置信传播方法。该算法通过在图模型结构中传递低秩局部消息来更新集成，继承了两种方法的优良特性。集成技术使GEnBP能处理高维状态、参数及复杂含噪的黑箱生成过程，而图模型中的局部消息传递机制则确保该方法适用于分布式计算并高效处理复杂依赖结构。当集成规模远小于推断维度时，GEnBP的优势尤为显著——这一场景常见于时空建模、图像处理及物理模型反演等领域。该方法适用于通用问题结构，可同时学习系统参数、观测参数及潜在状态变量。