Learning DAGs without imposing acyclicity

TL;DR

This paper proposes a novel approach to learning DAGs from data by framing the problem as a sparse matrix factorization, avoiding explicit acyclicity constraints, and demonstrating effective recovery and computational efficiency.

Contribution

It introduces an $ ext{l}_1$-penalized optimization method for DAG learning that bypasses the need for explicit acyclicity constraints, improving efficiency and scalability.

Findings

Effective recovery of true graphs using $ ext{l}_1$-penalization

Produces almost-DAG graphs in practice

Computationally efficient compared to classical methods

Abstract

We explore if it is possible to learn a directed acyclic graph (DAG) from data without imposing explicitly the acyclicity constraint. In particular, for Gaussian distributions, we frame structural learning as a sparse matrix factorization problem and we empirically show that solving an $\ell_1$-penalized optimization yields to good recovery of the true graph and, in general, to almost-DAG graphs. Moreover, this approach is computationally efficient and is not affected by the explosion of combinatorial complexity as in classical structural learning algorithms.