发表机构
Hasso Plattner Institute; University of Potsdam（哈索·普拉特纳研究所; 波茨坦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出直接消息近似（DMA）框架，通过直接近似因子到变量消息并定义一致性条件，在因子图上实现可处理的近似推断，避免了EP和VMP的缺陷，并验证了其在贝叶斯神经网络中产生数据稀疏区域更宽的不确定性。
AI 中文摘要
因子图上的近似消息传递是两类主导概率推断算法的基础：期望传播（EP）和变分消息传递（VMP）。两种方法都近似每个因子边上的边缘分布，这迫使采用迭代轮询调度，存在负精度消息的风险，并且对于VMP，在Dirac-delta因子处会坍缩为点估计。我们提出了直接消息近似（DMA），它直接近似因子到变量的消息，而不是边缘分布。对于可归一化因子，我们定义了一个一致性条件（要求当所有其他传入消息为Dirac-delta时精确），以指导消息构造。我们证明了一个主定理（适当消息，任意图），用消息KL界定了边缘KL，并给出了三个结构性推论：Dirac输入一致性、无EP式内循环迭代、无负精度消息。此外，我们证明了乘积因子固有不当后向消息的互补O(1/r^2)保证，其闭式处理此前一直未被解决。作为具体实例，我们为乘积因子和leaky-ReLU因子推导了显式DMA消息，并组装了一个贝叶斯神经网络（BNN）推断算法，每个训练样本只需一次前向/后向扫描，且无梯度学习率超参数，验证了结构性保证转化为在数据稀疏区域（包括模型失配情况下）变宽的不确定性。
英文摘要
Approximate message passing on factor graphs underlies two dominant families of probabilistic inference algorithms: expectation propagation (EP) and variational message passing (VMP). Both methods approximate the marginal at each factor edge, forcing an iterative round-robin schedule, risking negative-precision messages, and, for VMP, collapsing to point estimates at Dirac-delta factors. We introduce Direct Message Approximation (DMA), which approximates factor-to-variable messages directly rather than the marginal. For normalisable factors, we define a consistency condition (requiring exactness when all other incoming messages are Dirac deltas) to guide message construction. We prove a master theorem (proper messages, any graph) bounding marginal KL from message KL, with three structural corollaries: Dirac-input consistency, no EP-style inner-loop iteration, and no negative-precision messages. Further, we prove a complementary $O(1/r^2)$ guarantee for the inherently improper backward message of the product factor, whose closed-form treatment has resisted prior work. As a concrete instantiation, we derive explicit DMA messages for the product and leaky-ReLU factors and assemble a Bayesian neural network (BNN) inference algorithm with one forward/backward sweep per training example and no gradient learning-rate hyperparameter, validating that the structural guarantees translate to predictive uncertainty that widens in data-sparse regions, including under model mismatch.
CommentsSubmitted to ICLR 2027
