On the Identifiability and Estimation of Functional Causal Models in the Presence of Outcome-Dependent Selection

Kun Zhang, Jiji Zhang, Biwei Huang MPI, Bernhard Schoelkopf, Clark Glymour
Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, PMLR R14:821-830, 2016.

Abstract

We study the identification and estimation of functional causal models under selection bias, with a focus on the situation where the selection depends solely on the effect variable, which is known as outcome-dependent selection. We address two questions of identifiability: the identifiability of the causal direction between two variables in the presence of selection bias, and, given the causal direction, the identifiability of the model with outcome-dependent selection. Regarding the first, we show that in the framework of post-nonlinear causal models, once outcome-dependent selection is properly modeled, the causal direction between two variables is generically identifiable; regarding the second, we identify some mild conditions under which an additive noise causal model with outcome-dependent selection is to a large extent identifiable. We also propose two methods for estimating an additive noise model from data that are generated with outcome-dependent selection.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR14-zhang16a, title = {On the Identifiability and Estimation of Functional Causal Models in the Presence of Outcome-Dependent Selection}, author = {Zhang, Kun and Zhang, Jiji and MPI, Biwei Huang and Schoelkopf, Bernhard and Glymour, Clark}, booktitle = {Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence}, pages = {821--830}, year = {2016}, editor = {Ihler, Alexander and Janzing, Dominik}, volume = {R14}, series = {Proceedings of Machine Learning Research}, month = {25--29 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r14/main/assets/zhang16a/zhang16a.pdf}, url = {https://proceedings.mlr.press/r14/zhang16a.html}, abstract = {We study the identification and estimation of functional causal models under selection bias, with a focus on the situation where the selection depends solely on the effect variable, which is known as outcome-dependent selection. We address two questions of identifiability: the identifiability of the causal direction between two variables in the presence of selection bias, and, given the causal direction, the identifiability of the model with outcome-dependent selection. Regarding the first, we show that in the framework of post-nonlinear causal models, once outcome-dependent selection is properly modeled, the causal direction between two variables is generically identifiable; regarding the second, we identify some mild conditions under which an additive noise causal model with outcome-dependent selection is to a large extent identifiable. We also propose two methods for estimating an additive noise model from data that are generated with outcome-dependent selection.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T On the Identifiability and Estimation of Functional Causal Models in the Presence of Outcome-Dependent Selection %A Kun Zhang %A Jiji Zhang %A Biwei Huang MPI %A Bernhard Schoelkopf %A Clark Glymour %B Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2016 %E Alexander Ihler %E Dominik Janzing %F pmlr-vR14-zhang16a %I PMLR %P 821--830 %U https://proceedings.mlr.press/r14/zhang16a.html %V R14 %X We study the identification and estimation of functional causal models under selection bias, with a focus on the situation where the selection depends solely on the effect variable, which is known as outcome-dependent selection. We address two questions of identifiability: the identifiability of the causal direction between two variables in the presence of selection bias, and, given the causal direction, the identifiability of the model with outcome-dependent selection. Regarding the first, we show that in the framework of post-nonlinear causal models, once outcome-dependent selection is properly modeled, the causal direction between two variables is generically identifiable; regarding the second, we identify some mild conditions under which an additive noise causal model with outcome-dependent selection is to a large extent identifiable. We also propose two methods for estimating an additive noise model from data that are generated with outcome-dependent selection. %Z Reissued by PMLR on 04 October 2026.
APA
Zhang, K., Zhang, J., MPI, B.H., Schoelkopf, B. & Glymour, C.. (2016). On the Identifiability and Estimation of Functional Causal Models in the Presence of Outcome-Dependent Selection. Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R14:821-830 Available from https://proceedings.mlr.press/r14/zhang16a.html. Reissued by PMLR on 04 October 2026.

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