Learning Large DAGs by Combining Continuous Optimization and Feedback Arc Set Heuristics

TL;DR

This paper introduces scalable heuristics for learning large Bayesian network DAGs by combining continuous optimization with feedback arc set heuristics, enabling handling of thousands of variables efficiently.

Contribution

The paper presents novel scalable heuristics that integrate gradient descent and feedback arc set solutions for large-scale DAG learning in linear structural models.

Findings

Methods scale to thousands of variables

Achieve effective DAG learning in linear models

Combine optimization and combinatorial approaches

Abstract

Bayesian networks represent relations between variables using a directed acyclic graph (DAG). Learning the DAG is an NP-hard problem and exact learning algorithms are feasible only for small sets of variables. We propose two scalable heuristics for learning DAGs in the linear structural equation case. Our methods learn the DAG by alternating between unconstrained gradient descent-based step to optimize an objective function and solving a maximum acyclic subgraph problem to enforce acyclicity. Thanks to this decoupling, our methods scale up beyond thousands of variables.