Message passing on factor graphs is a powerful framework for probabilistic inference, which finds important applications in various scientific domains. The most wide-spread message passing scheme is the sum-product algorithm (SPA) which gives exact results on trees but often fails on graphs with many small cycles. We search for an alternative message passing algorithm that works particularly well on such cyclic graphs. Therefore, we challenge the extrinsic principle of the SPA, which loses its objective on graphs with cycles. We further replace the local SPA message update rule at the factor nodes of the underlying graph with a generic mapping, which is optimized in a data-driven fashion. These modifications lead to a considerable improvement in performance while preserving the simplicity of the SPA. We evaluate our method for two classes of cyclic graphs: the 2x2 fully connected Ising grid and factor graphs for symbol detection on linear communication channels with inter-symbol interference. To enable the method for large graphs as they occur in practical applications, we develop a novel loss function that is inspired by the Bethe approximation from statistical physics and allows for training in an unsupervised fashion.

翻译：在因子图上进行消息传递是概率推断的强大框架，在多个科学领域具有重要应用。最广泛使用的消息传递方案是和积算法（SPA），该算法在树结构上能给出精确结果，但在包含许多小环路的图上通常失效。我们探索一种替代性的消息传递算法，使其特别适用于这类带环图。为此，我们挑战和积算法（SPA）的“外推原则”，该原则在含环图上会失去其目标性。进一步地，我们将底层因子图中因子节点处的局部SPA消息更新规则替换为通用映射函数，并通过数据驱动方式进行优化。这些改进在保持SPA简洁性的同时显著提升了性能。我们针对两类带环图评估所提方法：2×2全连接伊辛网格以及存在码间干扰的线性通信信道符号检测对应的因子图。为使该方法适用于实际应用中出现的大规模图结构，我们受统计物理学中贝特近似启发，开发了一种新型损失函数，该函数支持无监督训练。