# The Causal Marginal Polytope for Bounding Treatment Effects

arXiv: https://arxiv.org/abs/2202.13851 · HTML: https://mlsanity.com/paper/2202.13851/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 9 of 9)

- [The Causal-Neural Connection: Expressiveness, Learnability, and Inference](https://mlsanity.com/paper/2107.00793/) (2021)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [A Class of Algorithms for General Instrumental Variable Models](https://mlsanity.com/paper/2006.06366/) (2020)
- [On the Testability of Causal Models with Latent and Instrumental Variables](https://mlsanity.com/paper/1302.4976/) (2013)
- [Margins of discrete Bayesian networks](https://mlsanity.com/paper/1501.02103/) (2015)
- [Deriving Bounds and Inequality Constraints Using LogicalRelations Among Counterfactuals](https://mlsanity.com/paper/2007.00628/) (2020)
- [Causal Inference through a Witness Protection Program](https://mlsanity.com/paper/1406.0531/) (2014)
- [The Inflation Technique Completely Solves the Causal Compatibility Problem](https://mlsanity.com/paper/1707.06476/) (2017)

## Built on by (most cited first, 3 of 3)

- [Towards Bounding Causal Effects under Markov Equivalence](https://mlsanity.com/paper/2311.07259/) (2023)
- [Bounding probabilities of causation through the causal marginal problem](https://mlsanity.com/paper/2304.02023/) (2023)
- [Tightening Bounds on Probabilities of Causation By Merging Datasets](https://mlsanity.com/paper/2310.08406/) (2023)

## Abstract (arXiv)

Due to unmeasured confounding, it is often not possible to identify causal effects from a postulated model. Nevertheless, we can ask for partial identification, which usually boils down to finding upper and lower bounds of a causal quantity of interest derived from all solutions compatible with the encoded structural assumptions. One appealing way to derive such bounds is by casting it in terms of a constrained optimization method that searches over all causal models compatible with evidence, as introduced in the classic work of Balke and Pearl (1994) for discrete data. Although by construction this guarantees tight bounds, it poses a formidable computational challenge. To cope with this issue, alternatives include algorithms that are not guaranteed to be tight, or by introducing restrictions on the class of models. In this paper, we introduce a novel alternative: inspired by ideas coming from belief propagation, we enforce compatibility between marginals of a causal model and data, without constructing a global causal model. We call this collection of locally consistent marginals the causal marginal polytope. As global independence constraints disappear when considering small dimensional tractable marginals, this also leads to a rethinking of how to elicit and express causal knowledge. We provide an explicit algorithm and implementation of this idea, and assess its practicality with numerical experiments.