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 the first fully continuous optimization 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. We also explore the use of neural networks and orthogonal basis expansions to model nonlinearities for general nonparametric models. Extensive empirical study confirms the necessity of nonlinear dependency and the advantage of continuous optimization for score-based learning.

该研究开发了一个框架，可用于从数据中学习稀疏的非参数有向无环图（DAG）。该方法基于最近对DAG进行的代数描述，该描述为分数为基础的DAG模型的学习提供了一个完全连续的程序，该程序通过线性结构方程模型（SEM）进行参数化。该框架适用于各种非参数和半参数模型，包括广义线性模型（GLMs）、加性噪声模型和索引模型等特殊情况。与现有方法不同，这个方法不需要特定的建模选择、损失函数或算法，它提供了一个完全通用的框架，可应用于一般的非线性模型和一般的可微分的损失函数，以及通用的黑盒优化例程。代码可在https网址处获得。

学习稀疏非参数DAG