  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.
