Optimal Kernel Choice for Score Function-based Causal Discovery

Wenjie Wang, Biwei Huang, Feng Liu, Xinge You, Tongliang Liu, Kun Zhang, Mingming Gong
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:50650-50668, 2024.

Abstract

Score-based methods have demonstrated their effectiveness in discovering causal relationships by scoring different causal structures based on their goodness of fit to the data. Recently, Huang et al. proposed a generalized score function that can handle general data distributions and causal relationships by modeling the relations in reproducing kernel Hilbert space (RKHS). The selection of an appropriate kernel within this score function is crucial for accurately characterizing causal relationships and ensuring precise causal discovery. However, the current method involves manual heuristic selection of kernel parameters, making the process tedious and less likely to ensure optimality. In this paper, we propose a kernel selection method within the generalized score function that automatically selects the optimal kernel that best fits the data. Specifically, we model the generative process of the variables involved in each step of the causal graph search procedure as a mixture of independent noise variables. Based on this model, we derive an automatic kernel selection method by maximizing the marginal likelihood of the variables involved in each search step. We conduct experiments on both synthetic data and real-world benchmarks, and the results demonstrate that our proposed method outperforms heuristic kernel selection methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-wang24aa, title = {Optimal Kernel Choice for Score Function-based Causal Discovery}, author = {Wang, Wenjie and Huang, Biwei and Liu, Feng and You, Xinge and Liu, Tongliang and Zhang, Kun and Gong, Mingming}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {50650--50668}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/wang24aa/wang24aa.pdf}, url = {https://proceedings.mlr.press/v235/wang24aa.html}, abstract = {Score-based methods have demonstrated their effectiveness in discovering causal relationships by scoring different causal structures based on their goodness of fit to the data. Recently, Huang et al. proposed a generalized score function that can handle general data distributions and causal relationships by modeling the relations in reproducing kernel Hilbert space (RKHS). The selection of an appropriate kernel within this score function is crucial for accurately characterizing causal relationships and ensuring precise causal discovery. However, the current method involves manual heuristic selection of kernel parameters, making the process tedious and less likely to ensure optimality. In this paper, we propose a kernel selection method within the generalized score function that automatically selects the optimal kernel that best fits the data. Specifically, we model the generative process of the variables involved in each step of the causal graph search procedure as a mixture of independent noise variables. Based on this model, we derive an automatic kernel selection method by maximizing the marginal likelihood of the variables involved in each search step. We conduct experiments on both synthetic data and real-world benchmarks, and the results demonstrate that our proposed method outperforms heuristic kernel selection methods.} }
Endnote
%0 Conference Paper %T Optimal Kernel Choice for Score Function-based Causal Discovery %A Wenjie Wang %A Biwei Huang %A Feng Liu %A Xinge You %A Tongliang Liu %A Kun Zhang %A Mingming Gong %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-wang24aa %I PMLR %P 50650--50668 %U https://proceedings.mlr.press/v235/wang24aa.html %V 235 %X Score-based methods have demonstrated their effectiveness in discovering causal relationships by scoring different causal structures based on their goodness of fit to the data. Recently, Huang et al. proposed a generalized score function that can handle general data distributions and causal relationships by modeling the relations in reproducing kernel Hilbert space (RKHS). The selection of an appropriate kernel within this score function is crucial for accurately characterizing causal relationships and ensuring precise causal discovery. However, the current method involves manual heuristic selection of kernel parameters, making the process tedious and less likely to ensure optimality. In this paper, we propose a kernel selection method within the generalized score function that automatically selects the optimal kernel that best fits the data. Specifically, we model the generative process of the variables involved in each step of the causal graph search procedure as a mixture of independent noise variables. Based on this model, we derive an automatic kernel selection method by maximizing the marginal likelihood of the variables involved in each search step. We conduct experiments on both synthetic data and real-world benchmarks, and the results demonstrate that our proposed method outperforms heuristic kernel selection methods.
APA
Wang, W., Huang, B., Liu, F., You, X., Liu, T., Zhang, K. & Gong, M.. (2024). Optimal Kernel Choice for Score Function-based Causal Discovery. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:50650-50668 Available from https://proceedings.mlr.press/v235/wang24aa.html.

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