We propose an efficient nonparametric strategy for learning a message operator in expectation propagation (EP), which takes as input the set of incoming messages to a factor node, and produces an outgoing message as output. This learned operator replaces the multivariate integral required in classical EP, which may not have an analytic expression. We use kernel-based regression, which is trained on a set of probability distributions representing the incoming messages, and the associated outgoing messages. The kernel approach has two main advantages: first, it is fast, as it is implemented using a novel two-layer random feature representation of the input message distributions; second, it has principled uncertainty estimates, and can be cheaply updated online, meaning it can request and incorporate new training data when it encounters inputs on which it is uncertain. In experiments, our approach is able to solve learning problems where a single message operator is required for multiple, substantially different data sets (logistic regression for a variety of classification problems), where the ability to accurately assess uncertainty and to efficiently and robustly update the message operator are essential.

提出了一种非参数学习Expectation Propagation（EP）中消息操作符的高效策略，该方法使用基于内核的回归，以代替经典EP中所需的多元积分，并具有原理性的不确定性估计，能够在遇到不确定的情况下快速更新，适用于具有多个数据集的学习问题，如逻辑回归分类问题。

基于核的即时学习，用于传递期望传播消息