We propose a novel method to optimize the structure of factor graphs for graph-based inference. As an example inference task, we consider symbol detection on linear inter-symbol interference channels. The factor graph framework has the potential to yield low-complexity symbol detectors. However, the sum-product algorithm on cyclic factor graphs is suboptimal and its performance is highly sensitive to the underlying graph. Therefore, we optimize the structure of the underlying factor graphs in an end-to-end manner using machine learning. For that purpose, we transform the structural optimization into a clustering problem of low-degree factor nodes that incorporates the known channel model into the optimization. Furthermore, we study the combination of this approach with neural belief propagation, yielding near-maximum a posteriori symbol detection performance for specific channels.

翻译：我们提出一种优化因子图结构的新方法，用于基于图的推理。以线性码间干扰信道上的符号检测为示例推理任务，因子图框架具有实现低复杂度符号检测器的潜力。然而，循环因子图上的和积算法并非最优，其性能高度依赖于底层图结构。因此，我们利用机器学习以端到端的方式优化底层因子图的结构。为此，我们将结构优化转化为低阶因子节点的聚类问题，该过程将已知信道模型纳入优化中。此外，我们研究了该方法与神经置信传播的结合，可在特定信道上实现接近最大后验概率的符号检测性能。