Constraint-Free Structure Learning with Smooth Acyclic Orientations

TL;DR

COSMO introduces a constraint-free, differentiable approach for acyclic structure learning that is faster and maintains high accuracy without explicit acyclicity constraints.

Contribution

It proposes a novel smooth orientation matrix parameterization that avoids explicit acyclicity constraints, ensuring convergence to acyclic solutions efficiently.

Findings

COSMO converges to acyclic solutions without explicit constraints.

It outperforms existing methods in graph reconstruction accuracy.

COSMO is computationally faster due to its constraint-free formulation.

Abstract

The structure learning problem consists of fitting data generated by a Directed Acyclic Graph (DAG) to correctly reconstruct its arcs. In this context, differentiable approaches constrain or regularize the optimization problem using a continuous relaxation of the acyclicity property. The computational cost of evaluating graph acyclicity is cubic on the number of nodes and significantly affects scalability. In this paper we introduce COSMO, a constraint-free continuous optimization scheme for acyclic structure learning. At the core of our method, we define a differentiable approximation of an orientation matrix parameterized by a single priority vector. Differently from previous work, our parameterization fits a smooth orientation matrix and the resulting acyclic adjacency matrix without evaluating acyclicity at any step. Despite the absence of explicit constraints, we prove that COSMO always converges to an acyclic solution. In addition to being asymptotically faster, our empirical analysis highlights how COSMO performance on graph reconstruction compares favorably with competing structure learning methods.