DAGs with NO TEARS: Continuous Optimization for Structure Learning

TL;DR

This paper introduces a novel continuous optimization approach for learning DAG structures, avoiding combinatorial constraints and enabling efficient, exact acyclicity enforcement, leading to improved performance over existing methods.

Contribution

It proposes a new smooth and exact characterization of DAG acyclicity, allowing continuous optimization for structure learning without structural assumptions.

Findings

Outperforms existing structure learning methods

Enables efficient and exact acyclicity enforcement

Provides open-source implementation

Abstract

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 \emph{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. Code implementing the proposed algorithm is open-source and publicly available at https://github.com/xunzheng/notears.