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：我们提出了一个优化基于图形的推断系数图结构的新颖方法。 作为例推, 我们考虑在线性符号间干扰通道上检测符号。 系数图框架有可能生成低复杂性符号检测器。 但是, 循环系数图上的总产品算法并不理想, 其性能对基本图非常敏感 。 因此, 我们使用机器学习, 以端到端的方式优化基本要素图的结构结构 。 为此, 我们将结构优化转化为低度系数节点的集成问题, 将已知的频道模型纳入优化 。 此外, 我们研究这一方法与神经信仰传播相结合, 产生特定频道的近乎极限的外延符号检测性能 。