Non-Parametric Path Analysis in Structural Causal Models

Junzhe Zhang, Elias Bareinboim
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:652-661, 2018.

Abstract

One of the fundamental tasks in causal inference is to decompose the observed association between a decision X and an outcome Y into its most basic structural mechanisms. In this paper, we introduce counterfactual measures for effects along with a specific mechanism, represented as a path from X to Y in an arbitrary structural causal model. We derive a novel non-parametric decomposition formula that expresses the covariance of X and Y as a sum over unblocked paths from X to Y contained in an arbitrary causal model. This formula allows a fine-grained path analysis without requiring a commitment to any particular parametric form, and can be seen as a generalization of Wright’s decomposition method in linear systems (1923,1932) and Pearl’s non-parametric mediation formula (2001).

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-zhang18b, title = {Non-Parametric Path Analysis in Structural Causal Models}, author = {Zhang, Junzhe and Bareinboim, Elias}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {652--661}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/zhang18b/zhang18b.pdf}, url = {https://proceedings.mlr.press/r16/zhang18b.html}, abstract = {One of the fundamental tasks in causal inference is to decompose the observed association between a decision X and an outcome Y into its most basic structural mechanisms. In this paper, we introduce counterfactual measures for effects along with a specific mechanism, represented as a path from X to Y in an arbitrary structural causal model. We derive a novel non-parametric decomposition formula that expresses the covariance of X and Y as a sum over unblocked paths from X to Y contained in an arbitrary causal model. This formula allows a fine-grained path analysis without requiring a commitment to any particular parametric form, and can be seen as a generalization of Wright’s decomposition method in linear systems (1923,1932) and Pearl’s non-parametric mediation formula (2001).}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Non-Parametric Path Analysis in Structural Causal Models %A Junzhe Zhang %A Elias Bareinboim %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-zhang18b %I PMLR %P 652--661 %U https://proceedings.mlr.press/r16/zhang18b.html %V R16 %X One of the fundamental tasks in causal inference is to decompose the observed association between a decision X and an outcome Y into its most basic structural mechanisms. In this paper, we introduce counterfactual measures for effects along with a specific mechanism, represented as a path from X to Y in an arbitrary structural causal model. We derive a novel non-parametric decomposition formula that expresses the covariance of X and Y as a sum over unblocked paths from X to Y contained in an arbitrary causal model. This formula allows a fine-grained path analysis without requiring a commitment to any particular parametric form, and can be seen as a generalization of Wright’s decomposition method in linear systems (1923,1932) and Pearl’s non-parametric mediation formula (2001). %Z Reissued by PMLR on 04 October 2026.
APA
Zhang, J. & Bareinboim, E.. (2018). Non-Parametric Path Analysis in Structural Causal Models. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:652-661 Available from https://proceedings.mlr.press/r16/zhang18b.html. Reissued by PMLR on 04 October 2026.

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