Learning Sparse Nonparametric DAGs

Xun Zheng, Chen Dan, Bryon Aragam, Pradeep Ravikumar, Eric Xing
; Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:3414-3425, 2020.

Abstract

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. 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.

Cite this Paper


BibTeX
@InProceedings{pmlr-v108-zheng20a, title = {Learning Sparse Nonparametric DAGs}, author = {Zheng, Xun and Dan, Chen and Aragam, Bryon and Ravikumar, Pradeep and Xing, Eric}, pages = {3414--3425}, year = {2020}, editor = {Silvia Chiappa and Roberto Calandra}, volume = {108}, series = {Proceedings of Machine Learning Research}, address = {Online}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/zheng20a/zheng20a.pdf}, url = {http://proceedings.mlr.press/v108/zheng20a.html}, abstract = {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. 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.} }
Endnote
%0 Conference Paper %T Learning Sparse Nonparametric DAGs %A Xun Zheng %A Chen Dan %A Bryon Aragam %A Pradeep Ravikumar %A Eric Xing %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-zheng20a %I PMLR %J Proceedings of Machine Learning Research %P 3414--3425 %U http://proceedings.mlr.press %V 108 %W PMLR %X 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. 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.
APA
Zheng, X., Dan, C., Aragam, B., Ravikumar, P. & Xing, E.. (2020). Learning Sparse Nonparametric DAGs. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in PMLR 108:3414-3425

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