Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables Under Monotonicity Assumptions

Naoya Hashimoto, Yuta Kawakami, Jin Tian
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:2827-2835, 2026.

Abstract

Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in settings with discrete treatment and discrete outcome. We propose new families of monotonicity assumptions and formulate the bounding problem as a linear programming problem. We further introduce a new monotonicity assumption specifically to achieve identification. Finally, we present numerical experiments to validate our methods and demonstrate their application using real-world datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-hashimoto26a, title = { Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables Under Monotonicity Assumptions }, author = {Hashimoto, Naoya and Kawakami, Yuta and Tian, Jin}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {2827--2835}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/hashimoto26a/hashimoto26a.pdf}, url = {https://proceedings.mlr.press/v300/hashimoto26a.html}, abstract = { Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in settings with discrete treatment and discrete outcome. We propose new families of monotonicity assumptions and formulate the bounding problem as a linear programming problem. We further introduce a new monotonicity assumption specifically to achieve identification. Finally, we present numerical experiments to validate our methods and demonstrate their application using real-world datasets. } }
Endnote
%0 Conference Paper %T Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables Under Monotonicity Assumptions %A Naoya Hashimoto %A Yuta Kawakami %A Jin Tian %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-hashimoto26a %I PMLR %P 2827--2835 %U https://proceedings.mlr.press/v300/hashimoto26a.html %V 300 %X Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in settings with discrete treatment and discrete outcome. We propose new families of monotonicity assumptions and formulate the bounding problem as a linear programming problem. We further introduce a new monotonicity assumption specifically to achieve identification. Finally, we present numerical experiments to validate our methods and demonstrate their application using real-world datasets.
APA
Hashimoto, N., Kawakami, Y. & Tian, J.. (2026). Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables Under Monotonicity Assumptions . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:2827-2835 Available from https://proceedings.mlr.press/v300/hashimoto26a.html.

Related Material