提出两种新框架，让期望传播始终满足可积性约束。
Avoiding Non-Integrable Beliefs in Expectation Propagation
- 允许消息非可积，但确保最终信念可积
- 在广义线性模型中实现更优信号恢复性能
- 适合需要严格概率一致性保证的推断场景
期望传播（EP）是一种广泛使用的迭代消息传递算法，将全局推断问题分解为多个局部问题，通过中间函数（消息）近似边缘分布为‘信念’。已有研究表明，EP 的驻点等价于对应的受限贝特自由能（BFE）优化问题，因此 EP 实质上是优化受限 BFE 的迭代方法。然而，该迭代过程可能偏离 BFE 优化问题的可行集，即信念不可积。现有文献通常采用多种手段强制所有消息可积，但这会缩小实际可行集。尤其在因子本身不可积的极端情况下，仅保证消息可积不足以使信念可积。本文提出两种新的 EP 框架，确保信念始终可积，且允许消息非可积。随后，我们利用所提方法研究了广义线性模型（GLM）中的信号恢复问题。
原文摘要 · Abstract (English)
Expectation Propagation (EP) is a widely used iterative message-passing algorithm that decomposes a global inference problem into multiple local ones. It approximates marginal distributions as ``beliefs'' using intermediate functions called ``messages''. It has been shown that the stationary points of EP are the same as corresponding constrained Bethe Free Energy (BFE) optimization problem. Therefore, EP is an iterative method of optimizing the constrained BFE. However, the iterative method may fall out of the feasible set of the BFE optimization problem, i.e., the beliefs are not integrable. In most literature, the authors use various methods to keep all the messages integrable. In most Bayesian estimation problems, limiting the messages to be integrable shrinks the actual feasible set. Furthermore, in extreme cases where the factors are not integrable, making the message itself integrable is not enough to have integrable beliefs. In this paper, two EP frameworks are proposed to ensure that EP has integrable beliefs. Both of the methods allows non-integrable messages. We then investigate the signal recovery problem in Generalized Linear Model (GLM) using our proposed methods.
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