Contextual Directed Acyclic Graphs

Ryan Thompson, Edwin V. Bonilla, Robert Kohn
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:2872-2880, 2024.

Abstract

Estimating the structure of directed acyclic graphs (DAGs) from observational data remains a significant challenge in machine learning. Most research in this area concentrates on learning a single DAG for the entire population. This paper considers an alternative setting where the graph structure varies across individuals based on available "contextual" features. We tackle this contextual DAG problem via a neural network that maps the contextual features to a DAG, represented as a weighted adjacency matrix. The neural network is equipped with a novel projection layer that ensures the output matrices are sparse and satisfy a recently developed characterization of acyclicity. We devise a scalable computational framework for learning contextual DAGs and provide a convergence guarantee and an analytical gradient for backpropagating through the projection layer. Our experiments suggest that the new approach can recover the true context-specific graph where existing approaches fail.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-thompson24a, title = {Contextual Directed Acyclic Graphs}, author = {Thompson, Ryan and V. Bonilla, Edwin and Kohn, Robert}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {2872--2880}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/thompson24a/thompson24a.pdf}, url = {https://proceedings.mlr.press/v238/thompson24a.html}, abstract = {Estimating the structure of directed acyclic graphs (DAGs) from observational data remains a significant challenge in machine learning. Most research in this area concentrates on learning a single DAG for the entire population. This paper considers an alternative setting where the graph structure varies across individuals based on available "contextual" features. We tackle this contextual DAG problem via a neural network that maps the contextual features to a DAG, represented as a weighted adjacency matrix. The neural network is equipped with a novel projection layer that ensures the output matrices are sparse and satisfy a recently developed characterization of acyclicity. We devise a scalable computational framework for learning contextual DAGs and provide a convergence guarantee and an analytical gradient for backpropagating through the projection layer. Our experiments suggest that the new approach can recover the true context-specific graph where existing approaches fail.} }
Endnote
%0 Conference Paper %T Contextual Directed Acyclic Graphs %A Ryan Thompson %A Edwin V. Bonilla %A Robert Kohn %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-thompson24a %I PMLR %P 2872--2880 %U https://proceedings.mlr.press/v238/thompson24a.html %V 238 %X Estimating the structure of directed acyclic graphs (DAGs) from observational data remains a significant challenge in machine learning. Most research in this area concentrates on learning a single DAG for the entire population. This paper considers an alternative setting where the graph structure varies across individuals based on available "contextual" features. We tackle this contextual DAG problem via a neural network that maps the contextual features to a DAG, represented as a weighted adjacency matrix. The neural network is equipped with a novel projection layer that ensures the output matrices are sparse and satisfy a recently developed characterization of acyclicity. We devise a scalable computational framework for learning contextual DAGs and provide a convergence guarantee and an analytical gradient for backpropagating through the projection layer. Our experiments suggest that the new approach can recover the true context-specific graph where existing approaches fail.
APA
Thompson, R., V. Bonilla, E. & Kohn, R.. (2024). Contextual Directed Acyclic Graphs. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:2872-2880 Available from https://proceedings.mlr.press/v238/thompson24a.html.

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