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Recently continuous relaxations have been proposed in order to learn DirectedAcyclic Graphs (DAGs) from data by backpropagation, instead of usingcombinatorial optimization. However, a number of techniques for fully discretebackpropagation could instead be applied. In this paper, we explore thatdirection and propose DAG-DB, a framework for learning DAGs by DiscreteBackpropagation. Based on the architecture of Implicit Maximum LikelihoodEstimation [I-MLE, arXiv:2106.01798], DAG-DB adopts a probabilistic approach tothe problem, sampling binary adjacency matrices from an implicit probabilitydistribution. DAG-DB learns a parameter for the distribution from the lossincurred by each sample, performing competitively using either of two fullydiscrete backpropagation techniques, namely I-MLE and Straight-ThroughEstimation.

Learning Discrete Directed Acyclic Graphs via Backpropagation