Causal Structure Learning With One-Dimensional Convolutional Neural Networks

Causal structure discovery has an important guiding role in explanatory artificial intelligence. In order to discover causal relationships from observed data and restore causal structure graphs, we propose the Directed Acyclic Graph structure learning with Causal Convolutional Neural Networks (DAG-CCNN). First, we employ a nonlinear structural causal model (SCM) generation mechanism and propose an integrated neural network model which combines a fully-connected (FC) layer and one-dimensional convolutional (1D-Conv) layer. Then, a new acyclic algebraic representation is proposed, and a theorem and its proof are given. We use the eigenvalues of the weighted adjacency matrix instead of the Hadamard product of the adjacency matrix to represent the acyclicity of the graph, which essentially avoids the computational complexity associated with matrix multiplication. Finally, compared with DAG-GNN, NOTEARS and GraN-DAG, the experimental results show that the DAG-CCNN method has some advantages in performance on synthetic and real Sach data sets and the results of the restoring causal structure graph are more satisfactory.