# Bounds on Causal Effects and Application to High Dimensional Data

arXiv: https://arxiv.org/abs/2106.12121 · HTML: https://mlsanity.com/paper/2106.12121/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 25 references that are in the map.
- First posted on arXiv 23 Jun 2021.

## Builds on (most cited first, 1 of 1)

- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)

## Built on by (most cited first, 22 of 22)

- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [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)
- [Rethinking Domain Generalization: Discriminability and Generalizability](https://mlsanity.com/paper/2309.16483/) (2023)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Unit Selection with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09569/) (2022)
- [Probabilities of Causation: Adequate Size of Experimental and Observational Samples](https://mlsanity.com/paper/2210.05027/) (2022)
- [Integrating Earth Observation Data into Causal Inference: Challenges and Opportunities](https://mlsanity.com/paper/2301.12985/) (2023)
- [Towards Bounding Causal Effects under Markov Equivalence](https://mlsanity.com/paper/2311.07259/) (2023)
- [Unit Selection: Learning Benefit Function from Finite Population Data](https://mlsanity.com/paper/2210.08203/) (2022)
- [Unit Selection: Case Study and Comparison with A/B Test Heuristic](https://mlsanity.com/paper/2210.05030/) (2022)
- [Probabilities of Causation: Role of Observational Data](https://mlsanity.com/paper/2210.08874/) (2022)
- [Estimating Causal Effects Under Image Confounding Bias with an Application to Poverty in Africa](https://mlsanity.com/paper/2206.06410/) (2022)
- [Epsilon-Identifiability of Causal Quantities](https://mlsanity.com/paper/2301.12022/) (2023)
- [Approximate Causal Effect Identification under Weak Confounding](https://mlsanity.com/paper/2306.13242/) (2023)
- [Risk-Averse Multi-Armed Bandits with Unobserved Confounders: A Case Study in Emotion Regulation in Mobile Health](https://mlsanity.com/paper/2209.04356/) (2022)
- [Unifying Invariant and Variant Features for Graph Out-of-Distribution via Probability of Necessity and Sufficiency](https://mlsanity.com/paper/2407.15273/) (2024)
- [Identification of Probabilities of Causation: from Recursive to Closed-Form Bounds](https://mlsanity.com/paper/2505.15274/) (2025)
- [Bounding Probabilities of Causation with Partial Causal Diagrams](https://mlsanity.com/paper/2602.14503/) (2026)
- [Causality-Based Feature Importance Quantifying Methods: PN-FI, PS-FI and PNS-FI](https://mlsanity.com/paper/2308.14474/) (2023)
- [A Computational Theory for Efficient Mini Agent Evaluation with Causal Guarantees](https://mlsanity.com/paper/2503.21138/) (2025)
- [Uncertainty-aware Causal Decision Making via Effect Bound Decomposition](https://mlsanity.com/paper/2601.22736/) (2026)

## Abstract (arXiv)

This paper addresses the problem of estimating causal effects when adjustment variables in the back-door or front-door criterion are partially observed. For such scenarios, we derive bounds on the causal effects by solving two non-linear optimization problems, and demonstrate that the bounds are sufficient. Using this optimization method, we propose a framework for dimensionality reduction that allows one to trade bias for estimation power, and demonstrate its performance using simulation studies.