Learning Sparse Nonparametric DAGs

About

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.

Xun Zheng, Chen Dan, Bryon Aragam, Pradeep Ravikumar, Eric P. Xing · 2019

Related benchmarks

Task	Dataset	Result
DAG Structure Recovery	non-linear-1 5000 samples	SHD5.2	48
Causal Discovery	Sachs real-world data protein signaling network	SHD13	41
Causal Discovery	Synthetic Temporal Sequences	SHD6.36	40
Causal Discovery	Alarm d=37	Mod. SHD54	21
Causal Discovery	Cancer n=5	Structural Hamming Distance (SHD)3	14
Causal Discovery	Barley n=48	SHD85	14
Causal Discovery	Win95pts	SHD133	14
Causal Discovery	Insurance n=27	SHD60	14
Causal Discovery	Water n=32	SHD61	14
Causal Discovery	non-linear-2 d=10, 5000 samples (test)	SHD5.4	12