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.

高维模型中的高效推理是机器学习中的一大挑战。本文介绍了高斯集成信念传播算法（GEnBP），它是集合卡尔曼滤波器和高斯信念传播方法的融合。GEnBP通过图模型结构中的低秩局部消息传递来更新集合，结合了每种方法的优点，能够处理高维状态、参数和复杂、嘈杂、黑盒子生成过程。GEnBP特别适用于集合大小远小于推理维度的情况，常见于时空建模、图像处理和物理模型反演等领域。GEnBP可应用于包括联合学习系统参数、观测参数和潜在状态变量在内的一般问题结构。

高维系统高效推理的高斯集成置信传播