Learning Discrete Directed Acyclic Graphs via Backpropagation
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.
Cite
@article{arxiv.2210.15353,
title = {Learning Discrete Directed Acyclic Graphs via Backpropagation},
author = {Andrew J. Wren and Pasquale Minervini and Luca Franceschi and Valentina Zantedeschi},
journal= {arXiv preprint arXiv:2210.15353},
year = {2022}
}
Comments
15 pages, 2 figures, 7 tables. Accepted for NeurIPS 2022 workshops on: Causal Machine Learning for Real-World Impact; and Neuro Causal and Symbolic AI