Sensitivity Analysis of Linear Structural Causal Models

Carlos Cinelli, Daniel Kumor, Bryant Chen, Judea Pearl, Elias Bareinboim
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:1252-1261, 2019.

Abstract

Causal inference requires assumptions about the data generating process, many of which are unverifiable from the data. Given that some causal assumptions might be uncertain or disputed, formal methods are needed to quantify how sensitive research conclusions are to violations of those assumptions. Although an extensive literature exists on the topic, most results are limited to specific model structures, while a general-purpose algorithmic framework for sensitivity analysis is still lacking. In this paper, we develop a formal, systematic approach to sensitivity analysis for arbitrary linear Structural Causal Models (SCMs). We start by formalizing sensitivity analysis as a constrained identification problem. We then develop an efficient, graph-based identification algorithm that exploits non-zero constraints on both directed and bidirected edges. This allows researchers to systematically derive sensitivity curves for a target causal quantity with an arbitrary set of path coefficients and error covariances as sensitivity parameters. These results can be used to display the degree to which violations of causal assumptions affect the target quantity of interest, and to judge, on scientific grounds, whether problematic degrees of violations are plausible.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-cinelli19a, title = {Sensitivity Analysis of Linear Structural Causal Models}, author = {Cinelli, Carlos and Kumor, Daniel and Chen, Bryant and Pearl, Judea and Bareinboim, Elias}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {1252--1261}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/cinelli19a/cinelli19a.pdf}, url = {https://proceedings.mlr.press/v97/cinelli19a.html}, abstract = {Causal inference requires assumptions about the data generating process, many of which are unverifiable from the data. Given that some causal assumptions might be uncertain or disputed, formal methods are needed to quantify how sensitive research conclusions are to violations of those assumptions. Although an extensive literature exists on the topic, most results are limited to specific model structures, while a general-purpose algorithmic framework for sensitivity analysis is still lacking. In this paper, we develop a formal, systematic approach to sensitivity analysis for arbitrary linear Structural Causal Models (SCMs). We start by formalizing sensitivity analysis as a constrained identification problem. We then develop an efficient, graph-based identification algorithm that exploits non-zero constraints on both directed and bidirected edges. This allows researchers to systematically derive sensitivity curves for a target causal quantity with an arbitrary set of path coefficients and error covariances as sensitivity parameters. These results can be used to display the degree to which violations of causal assumptions affect the target quantity of interest, and to judge, on scientific grounds, whether problematic degrees of violations are plausible.} }
Endnote
%0 Conference Paper %T Sensitivity Analysis of Linear Structural Causal Models %A Carlos Cinelli %A Daniel Kumor %A Bryant Chen %A Judea Pearl %A Elias Bareinboim %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-cinelli19a %I PMLR %P 1252--1261 %U https://proceedings.mlr.press/v97/cinelli19a.html %V 97 %X Causal inference requires assumptions about the data generating process, many of which are unverifiable from the data. Given that some causal assumptions might be uncertain or disputed, formal methods are needed to quantify how sensitive research conclusions are to violations of those assumptions. Although an extensive literature exists on the topic, most results are limited to specific model structures, while a general-purpose algorithmic framework for sensitivity analysis is still lacking. In this paper, we develop a formal, systematic approach to sensitivity analysis for arbitrary linear Structural Causal Models (SCMs). We start by formalizing sensitivity analysis as a constrained identification problem. We then develop an efficient, graph-based identification algorithm that exploits non-zero constraints on both directed and bidirected edges. This allows researchers to systematically derive sensitivity curves for a target causal quantity with an arbitrary set of path coefficients and error covariances as sensitivity parameters. These results can be used to display the degree to which violations of causal assumptions affect the target quantity of interest, and to judge, on scientific grounds, whether problematic degrees of violations are plausible.
APA
Cinelli, C., Kumor, D., Chen, B., Pearl, J. & Bareinboim, E.. (2019). Sensitivity Analysis of Linear Structural Causal Models. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:1252-1261 Available from https://proceedings.mlr.press/v97/cinelli19a.html.

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