Learning Large DAGs by Combining Continuous Optimization and Feedback Arc Set Heuristics
This work addresses the scalability bottleneck in learning DAGs for Bayesian networks, which is incremental as it builds on existing optimization and acyclicity enforcement methods.
The authors tackled the NP-hard problem of learning Bayesian network DAGs by proposing two scalable heuristics that combine continuous optimization with feedback arc set techniques, enabling scaling to thousands of variables in linear structural equation models.
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.