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

arXiv: https://arxiv.org/abs/2602.18762 · HTML: https://mlsanity.com/paper/2602.18762/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 44 references that are in the map.
- First posted on arXiv 21 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (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)
- [Probabilities of Causation with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09568/) (2022)
- [Structural Causal Models Are (Solvable by) Credal Networks](https://mlsanity.com/paper/2008.00463/) (2020)
- [A General Method for Deriving Tight Symbolic Bounds on Causal Effects](https://mlsanity.com/paper/2003.10702/) (2020)
- [Optimal Treatment Allocation for Efficient Policy Evaluation in Sequential Decision Making](https://mlsanity.com/paper/2311.02532/) (2023)
- [Efficient Computation of Counterfactual Bounds](https://mlsanity.com/paper/2307.08304/) (2023)
- [Probabilities of Causation for Continuous and Vector Variables](https://mlsanity.com/paper/2405.20487/) (2024)
- [Scalable Computation of Causal Bounds](https://mlsanity.com/paper/2308.02709/) (2023)
- [Bounding the Probability of Causation in Mediation Analysis](https://mlsanity.com/paper/1411.2636/) (2014)
- [Moments of Causal Effects](https://mlsanity.com/paper/2505.04971/) (2025)
- [Decomposition of Probabilities of Causation with Two Mediators](https://mlsanity.com/paper/2505.04983/) (2025)
- [Multilinear and Linear Programs for Partially Identifiable Queries in Quasi-Markovian Structural Causal Models](https://mlsanity.com/paper/2509.03548/) (2025)

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

- [Identification and Bounding of Central Moments of Causal Effects Using Marginal Moments Information](https://mlsanity.com/paper/2607.04957/) (2026)

## Abstract (arXiv)

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 ordinal 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.