# Towards Bounding Causal Effects under Markov Equivalence

arXiv: https://arxiv.org/abs/2311.07259 · HTML: https://mlsanity.com/paper/2311.07259/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 45 references that are in the map.
- First posted on arXiv 13 Nov 2023.

## Builds on (most cited first, 10 of 10)

- [PC-Fairness: A Unified Framework for Measuring Causality-based Fairness](https://mlsanity.com/paper/1910.12586/) (2019)
- [Strong Completeness and Faithfulness in Bayesian Networks](https://mlsanity.com/paper/1302.4973/) (2013)
- [Stochastic Causal Programming for Bounding Treatment Effects](https://mlsanity.com/paper/2202.10806/) (2022)
- [Bounds on Causal Effects and Application to High Dimensional Data](https://mlsanity.com/paper/2106.12121/) (2021)
- [Partial Identification of Treatment Effects with Implicit Generative Models](https://mlsanity.com/paper/2210.08139/) (2022)
- [Causal Identification under Markov Equivalence](https://mlsanity.com/paper/1812.06209/) (2018)
- [Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding](https://mlsanity.com/paper/2103.15106/) (2021)
- [Deriving Bounds and Inequality Constraints Using LogicalRelations Among Counterfactuals](https://mlsanity.com/paper/2007.00628/) (2020)
- [Efficient Enumeration of Markov Equivalent DAGs](https://mlsanity.com/paper/2301.12212/) (2023)
- [The Causal Marginal Polytope for Bounding Treatment Effects](https://mlsanity.com/paper/2202.13851/) (2022)

## Built on by (most cited first, 8 of 8)

- [General agents contain world models](https://mlsanity.com/paper/2506.01622/) (2025)
- [Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning](https://mlsanity.com/paper/2507.05526/) (2025)
- [Consistency of Neural Causal Partial Identification](https://mlsanity.com/paper/2405.15673/) (2024)
- [The Limits of Predicting Agents from Behaviour](https://mlsanity.com/paper/2506.02923/) (2025)
- [Foundation Models for Partial Causal Identification](https://mlsanity.com/paper/2608.20841/) (2026)
- [Your Assumed DAG is Wrong and Here's How To Deal With It](https://mlsanity.com/paper/2502.17030/) (2025)
- [Root Cause Analysis with Latent Confounders using Partial Ancestral Graphs](https://mlsanity.com/paper/2606.20912/) (2026)
- [Two Layers of Instability in Causal Estimation](https://mlsanity.com/paper/2606.21185/) (2026)

## Abstract (arXiv)

Predicting the effect of unseen interventions is a fundamental research question across the data sciences. It is well established that in general such questions cannot be answered definitively from observational data. This realization has fuelled a growing literature introducing various identifying assumptions, for example in the form of a causal diagram among relevant variables. In practice, this paradigm is still too rigid for many practical applications as it is generally not possible to confidently delineate the true causal diagram. In this paper, we consider the derivation of bounds on causal effects given only observational data. We propose to take as input a less informative structure known as a Partial Ancestral Graph, which represents a Markov equivalence class of causal diagrams and is learnable from data. In this more ``data-driven'' setting, we provide a systematic algorithm to derive bounds on causal effects that exploit the invariant properties of the equivalence class, and that can be computed analytically. We demonstrate our method with synthetic and real data examples.