Learning Discrete Directed Acyclic Graphs via Backpropagation

TL;DR

This paper introduces DAG-DB, a novel framework for learning directed acyclic graphs (DAGs) using fully discrete backpropagation techniques, leveraging probabilistic sampling and implicit maximum likelihood estimation.

Contribution

It proposes a new discrete backpropagation framework for DAG learning, combining probabilistic sampling with I-MLE and Straight-Through Estimation methods.

Findings

DAG-DB performs competitively with existing methods.

The framework effectively learns DAG structures from data.

It demonstrates the viability of fully discrete backpropagation for DAGs.

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.