DAGs with NO TEARS: Continuous Optimization for Structure Learning
This addresses the problem of scalable and accurate DAG structure learning for researchers and practitioners in fields like causal inference and Bayesian networks, representing a new paradigm rather than an incremental improvement.
The paper tackles the combinatorial challenge of learning directed acyclic graph (DAG) structures by reformulating it as a continuous optimization problem using a novel smooth and exact acyclicity characterization, enabling efficient solving with standard algorithms and outperforming existing methods without structural assumptions.
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.