Learning Sparse Nonparametric DAGs
This provides a flexible method for causal inference and graphical modeling in fields like statistics and machine learning, though it is incremental as it builds on prior algebraic characterizations.
The paper tackles the problem of learning sparse nonparametric directed acyclic graphs (DAGs) from data by extending an algebraic characterization to nonparametric structural equation models, resulting in a general framework applicable to various nonlinear models and loss functions.
We develop a framework for learning sparse nonparametric directed acyclic graphs (DAGs) from data. Our approach is based on a recent algebraic characterization of DAGs that led to a fully continuous program for score-based learning of DAG models parametrized by a linear structural equation model (SEM). We extend this algebraic characterization to nonparametric SEM by leveraging nonparametric sparsity based on partial derivatives, resulting in a continuous optimization problem that can be applied to a variety of nonparametric and semiparametric models including GLMs, additive noise models, and index models as special cases. Unlike existing approaches that require specific modeling choices, loss functions, or algorithms, we present a completely general framework that can be applied to general nonlinear models (e.g. without additive noise), general differentiable loss functions, and generic black-box optimization routines. The code is available at https://github.com/xunzheng/notears.