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arXiv · 2210.15353

Learning Discrete Directed Acyclic Graphs via Backpropagation

Andrew J. Wren·Pasquale Minervini·Luca Franceschi·Valentina Zantedeschi
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Abstract

Recently continuous relaxations have been proposed in order to learn Directed Acyclic Graphs (DAGs) from data by backpropagation, instead of using combinatorial optimization. However, a number of techniques for fully discrete backpropagation could instead be applied. In this paper, we explore that direction and propose DAG-DB, a framework for learning DAGs by Discrete Backpropagation. Based on the architecture of Implicit Maximum Likelihood Estimation [I-MLE, arXiv:2106.01798], DAG-DB adopts a probabilistic approach to the problem, sampling binary adjacency matrices from an implicit probability distribution. DAG-DB learns a parameter for the distribution from the loss incurred by each sample, performing competitively using either of two fully discrete backpropagation techniques, namely I-MLE and Straight-Through Estimation.

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Andrew J. Wren, Pasquale Minervini, Luca Franceschi, Valentina Zantedeschi. 2022-10-27. Learning Discrete Directed Acyclic Graphs via Backpropagation. https://arxiv.org/abs/2210.15353

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