# Tightening Bounds on Probabilities of Causation By Merging Datasets

arXiv: https://arxiv.org/abs/2310.08406 · HTML: https://mlsanity.com/paper/2310.08406/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 12 Oct 2023.

## Builds on (most cited first, 13 of 13)

- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [A causal framework for distribution generalization](https://mlsanity.com/paper/2006.07433/) (2020)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [Personalized Decision Making -- A Conceptual Introduction](https://mlsanity.com/paper/2208.09558/) (2022)
- [Stochastic Causal Programming for Bounding Treatment Effects](https://mlsanity.com/paper/2202.10806/) (2022)
- [Probabilities of Causation with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09568/) (2022)
- [Causal Inference Through the Structural Causal Marginal Problem](https://mlsanity.com/paper/2202.01300/) (2022)
- [A General Method for Deriving Tight Symbolic Bounds on Causal Effects](https://mlsanity.com/paper/2003.10702/) (2020)
- [The Causal Marginal Polytope for Bounding Treatment Effects](https://mlsanity.com/paper/2202.13851/) (2022)

## Built on by (most cited first, 1 of 1)

- [Compositional Causal Reasoning Evaluation in Language Models](https://mlsanity.com/paper/2503.04556/) (2025)

## Abstract (arXiv)

Probabilities of Causation (PoC) play a fundamental role in decision-making in law, health care and public policy. Nevertheless, their point identification is challenging, requiring strong assumptions, in the absence of which only bounds can be derived. Existing work to further tighten these bounds by leveraging extra information either provides numerical bounds, symbolic bounds for fixed dimensionality, or requires access to multiple datasets that contain the same treatment and outcome variables. However, in many clinical, epidemiological and public policy applications, there exist external datasets that examine the effect of different treatments on the same outcome variable, or study the association between covariates and the outcome variable. These external datasets cannot be used in conjunction with the aforementioned bounds, since the former may entail different treatment assignment mechanisms, or even obey different causal structures. Here, we provide symbolic bounds on the PoC for this challenging scenario. We focus on combining either two randomized experiments studying different treatments, or a randomized experiment and an observational study, assuming causal sufficiency. Our symbolic bounds work for arbitrary dimensionality of covariates and treatment, and we discuss the conditions under which these bounds are tighter than existing bounds in literature. Finally, our bounds parameterize the difference in treatment assignment mechanism across datasets, allowing the mechanisms to vary across datasets while still allowing causal information to be transferred from the external dataset to the target dataset.