Optimization problem

Parameterized complexity

Line graph

Bayesian network

Treewidth

Artificial intelligence

Pathwidth

Graph

Directed graph

Mathematics

Mathematical optimization

Computer science

Directed acyclic graph

Algorithm

Theoretical computer science

Heuristics

Combinatorial optimization

Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches rely on various local heuristics for enforcing the acyclicity constraint. In this paper, we introduce a fundamentally different strategy: we formulate the structure learning problem as a purely continuous optimization problem over real matrices that avoids this combinatorial constraint entirely. This is achieved by a novel characterization of acyclicity that is not only smooth but also exact. The resulting problem can be efficiently solved by standard numerical algorithms, which also makes implementation effortless. The proposed method outperforms existing ones, without imposing any structural assumptions on the graph such as bounded treewidth or in-degree.

DAGs with NO TEARS: Continuous Optimization for Structure Learning