Causal Discovery with Mixed Linear and Nonlinear Additive Noise Models: A Scalable Approach

Wenqin Liu, Biwei Huang, Erdun Gao, Qiuhong Ke, Howard Bondell, Mingming Gong
Proceedings of the Third Conference on Causal Learning and Reasoning, PMLR 236:1237-1263, 2024.

Abstract

Estimating the structure of directed acyclic graphs (DAGs) from observational data is challenging due to the super-exponential growth of the search space with the number of nodes. Previous research primarily focuses on identifying a unique DAG under specific model constraints in linear or nonlinear scenarios. However, real-world scenarios often involve causal mechanisms with a mixture of linear and nonlinear characteristics, which has received limited attention in existing literature. Due to unidentifiability, existing algorithms relying on fully identifiable conditions may produce erroneous results. Although traditional methods like the PC algorithm can be employed to uncover such graphs, they typically yield only a Markov equivalence class. This paper introduces a novel causal discovery approach that extends beyond the Markov equivalence class, aiming to uncover as many edge directions as possible when the causal graph is not fully identifiable. Our approach exploits the second derivative of the log-likelihood in observational data, harnessing scalable machine learning approaches to approximate the score function. Overall, our approach demonstrates competitive accuracy comparable to current state-of-the-art techniques while offering a significant improvement in computational speed.

Cite this Paper

BibTeX
@InProceedings{pmlr-v236-liu24b, title = {Causal Discovery with Mixed Linear and Nonlinear Additive Noise Models: A Scalable Approach}, author = {Liu, Wenqin and Huang, Biwei and Gao, Erdun and Ke, Qiuhong and Bondell, Howard and Gong, Mingming}, booktitle = {Proceedings of the Third Conference on Causal Learning and Reasoning}, pages = {1237--1263}, year = {2024}, editor = {Locatello, Francesco and Didelez, Vanessa}, volume = {236}, series = {Proceedings of Machine Learning Research}, month = {01--03 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v236/liu24b/liu24b.pdf}, url = {https://proceedings.mlr.press/v236/liu24b.html}, abstract = {Estimating the structure of directed acyclic graphs (DAGs) from observational data is challenging due to the super-exponential growth of the search space with the number of nodes. Previous research primarily focuses on identifying a unique DAG under specific model constraints in linear or nonlinear scenarios. However, real-world scenarios often involve causal mechanisms with a mixture of linear and nonlinear characteristics, which has received limited attention in existing literature. Due to unidentifiability, existing algorithms relying on fully identifiable conditions may produce erroneous results. Although traditional methods like the PC algorithm can be employed to uncover such graphs, they typically yield only a Markov equivalence class. This paper introduces a novel causal discovery approach that extends beyond the Markov equivalence class, aiming to uncover as many edge directions as possible when the causal graph is not fully identifiable. Our approach exploits the second derivative of the log-likelihood in observational data, harnessing scalable machine learning approaches to approximate the score function. Overall, our approach demonstrates competitive accuracy comparable to current state-of-the-art techniques while offering a significant improvement in computational speed.} }
Endnote
%0 Conference Paper %T Causal Discovery with Mixed Linear and Nonlinear Additive Noise Models: A Scalable Approach %A Wenqin Liu %A Biwei Huang %A Erdun Gao %A Qiuhong Ke %A Howard Bondell %A Mingming Gong %B Proceedings of the Third Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2024 %E Francesco Locatello %E Vanessa Didelez %F pmlr-v236-liu24b %I PMLR %P 1237--1263 %U https://proceedings.mlr.press/v236/liu24b.html %V 236 %X Estimating the structure of directed acyclic graphs (DAGs) from observational data is challenging due to the super-exponential growth of the search space with the number of nodes. Previous research primarily focuses on identifying a unique DAG under specific model constraints in linear or nonlinear scenarios. However, real-world scenarios often involve causal mechanisms with a mixture of linear and nonlinear characteristics, which has received limited attention in existing literature. Due to unidentifiability, existing algorithms relying on fully identifiable conditions may produce erroneous results. Although traditional methods like the PC algorithm can be employed to uncover such graphs, they typically yield only a Markov equivalence class. This paper introduces a novel causal discovery approach that extends beyond the Markov equivalence class, aiming to uncover as many edge directions as possible when the causal graph is not fully identifiable. Our approach exploits the second derivative of the log-likelihood in observational data, harnessing scalable machine learning approaches to approximate the score function. Overall, our approach demonstrates competitive accuracy comparable to current state-of-the-art techniques while offering a significant improvement in computational speed.
APA
Liu, W., Huang, B., Gao, E., Ke, Q., Bondell, H. & Gong, M.. (2024). Causal Discovery with Mixed Linear and Nonlinear Additive Noise Models: A Scalable Approach. Proceedings of the Third Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 236:1237-1263 Available from https://proceedings.mlr.press/v236/liu24b.html.

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