Deriving Bounds And Inequality Constraints Using Logical Relations Among Counterfactuals

Noam Finkelstein, Ilya Shpitser
Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 124:1348-1357, 2020.

Abstract

Causal parameters may not be point identified in the presence of unobserved confounding. However, information about non-identified parameters, in the form of bounds, may still be recovered from the observed data in some cases. We develop a new general method for obtaining bounds on causal parameters using rules of probability and restrictions on counterfactuals implied by causal graphical models. We additionally provide inequality constraints on functionals of the observed data law implied by such causal models. Our approach is motivated by the observation that logical relations between identified and non-identified counterfactual events often yield information about non-identified events. We show that this approach is powerful enough to recover known sharp bounds and tight inequality constraints, and to derive novel bounds and constraints.

Cite this Paper


BibTeX
@InProceedings{pmlr-v124-finkelstein20a, title = {Deriving Bounds And Inequality Constraints Using Logical Relations Among Counterfactuals}, author = {Finkelstein, Noam and Shpitser, Ilya}, booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)}, pages = {1348--1357}, year = {2020}, editor = {Jonas Peters and David Sontag}, volume = {124}, series = {Proceedings of Machine Learning Research}, month = {03--06 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v124/finkelstein20a/finkelstein20a.pdf}, url = { http://proceedings.mlr.press/v124/finkelstein20a.html }, abstract = { Causal parameters may not be point identified in the presence of unobserved confounding. However, information about non-identified parameters, in the form of bounds, may still be recovered from the observed data in some cases. We develop a new general method for obtaining bounds on causal parameters using rules of probability and restrictions on counterfactuals implied by causal graphical models. We additionally provide inequality constraints on functionals of the observed data law implied by such causal models. Our approach is motivated by the observation that logical relations between identified and non-identified counterfactual events often yield information about non-identified events. We show that this approach is powerful enough to recover known sharp bounds and tight inequality constraints, and to derive novel bounds and constraints.} }
Endnote
%0 Conference Paper %T Deriving Bounds And Inequality Constraints Using Logical Relations Among Counterfactuals %A Noam Finkelstein %A Ilya Shpitser %B Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI) %C Proceedings of Machine Learning Research %D 2020 %E Jonas Peters %E David Sontag %F pmlr-v124-finkelstein20a %I PMLR %P 1348--1357 %U http://proceedings.mlr.press/v124/finkelstein20a.html %V 124 %X Causal parameters may not be point identified in the presence of unobserved confounding. However, information about non-identified parameters, in the form of bounds, may still be recovered from the observed data in some cases. We develop a new general method for obtaining bounds on causal parameters using rules of probability and restrictions on counterfactuals implied by causal graphical models. We additionally provide inequality constraints on functionals of the observed data law implied by such causal models. Our approach is motivated by the observation that logical relations between identified and non-identified counterfactual events often yield information about non-identified events. We show that this approach is powerful enough to recover known sharp bounds and tight inequality constraints, and to derive novel bounds and constraints.
APA
Finkelstein, N. & Shpitser, I.. (2020). Deriving Bounds And Inequality Constraints Using Logical Relations Among Counterfactuals. Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), in Proceedings of Machine Learning Research 124:1348-1357 Available from http://proceedings.mlr.press/v124/finkelstein20a.html .

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