# Scalable Computation of Causal Bounds

arXiv: https://arxiv.org/abs/2308.02709 · HTML: https://mlsanity.com/paper/2308.02709/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 4 Aug 2023.

## Builds on (most cited first, 15 of 15)

- [The Blessings of Multiple Causes](https://mlsanity.com/paper/1805.06826/) (2018)
- [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)
- [A Class of Algorithms for General Instrumental Variable Models](https://mlsanity.com/paper/2006.06366/) (2020)
- [A General Method for Deriving Tight Symbolic Bounds on Causal Effects](https://mlsanity.com/paper/2003.10702/) (2020)
- [Comment on "Blessings of Multiple Causes"](https://mlsanity.com/paper/1910.05438/) (2019)
- [Detecting confounding in multivariate linear models via spectral analysis](https://mlsanity.com/paper/1704.01430/) (2017)
- [Multiple Causal Inference with Latent Confounding](https://mlsanity.com/paper/1805.08273/) (2018)
- [Nonparametric Bounds and Sensitivity Analysis of Treatment Effects](https://mlsanity.com/paper/1503.01598/) (2015)
- [Implicit Causal Models for Genome-wide Association Studies](https://mlsanity.com/paper/1710.10742/) (2017)
- [Partial Identifiability in Discrete Data With Measurement Error](https://mlsanity.com/paper/2012.12449/) (2020)
- [Quantifier Elimination for Statistical Problems](https://mlsanity.com/paper/1301.6698/) (2013)
- [Deriving Bounds and Inequality Constraints Using LogicalRelations Among Counterfactuals](https://mlsanity.com/paper/2007.00628/) (2020)
- [Discussion of "The Blessings of Multiple Causes" by Wang and Blei](https://mlsanity.com/paper/1910.06991/) (2019)

## Built on by (most cited first, 5 of 5)

- [Multilinear and Linear Programs for Partially Identifiable Queries in Quasi-Markovian Structural Causal Models](https://mlsanity.com/paper/2509.03548/) (2025)
- [Information-Theoretic Causal Bounds under Unmeasured Confounding](https://mlsanity.com/paper/2601.17160/) (2026)
- [Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables under Monotonicity Assumptions](https://mlsanity.com/paper/2602.18762/) (2026)
- [Optimal Experiments for Partial Causal Effect Identification](https://mlsanity.com/paper/2605.06993/) (2026)
- [Identification and Bounding of Central Moments of Causal Effects Using Marginal Moments Information](https://mlsanity.com/paper/2607.04957/) (2026)

## Abstract (arXiv)

We consider the problem of computing bounds for causal queries on causal graphs with unobserved confounders and discrete valued observed variables, where identifiability does not hold. Existing non-parametric approaches for computing such bounds use linear programming (LP) formulations that quickly become intractable for existing solvers because the size of the LP grows exponentially in the number of edges in the causal graph. We show that this LP can be significantly pruned, allowing us to compute bounds for significantly larger causal inference problems compared to existing techniques. This pruning procedure allows us to compute bounds in closed form for a special class of problems, including a well-studied family of problems where multiple confounded treatments influence an outcome. We extend our pruning methodology to fractional LPs which compute bounds for causal queries which incorporate additional observations about the unit. We show that our methods provide significant runtime improvement compared to benchmarks in experiments and extend our results to the finite data setting. For causal inference without additional observations, we propose an efficient greedy heuristic that produces high quality bounds, and scales to problems that are several orders of magnitude larger than those for which the pruned LP can be solved.