# Stochastic Causal Programming for Bounding Treatment Effects

arXiv: https://arxiv.org/abs/2202.10806 · HTML: https://mlsanity.com/paper/2202.10806/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 74 references that are in the map.
- First posted on arXiv 22 Feb 2022.

## Builds on (most cited first, 24 of 24)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Avoiding Discrimination through Causal Reasoning](https://mlsanity.com/paper/1706.02744/) (2017)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [PC-Fairness: A Unified Framework for Measuring Causality-based Fairness](https://mlsanity.com/paper/1910.12586/) (2019)
- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [Neural Network Approximation: Three Hidden Layers Are Enough](https://mlsanity.com/paper/2010.14075/) (2020)
- [Confounding-Robust Policy Evaluation in Infinite-Horizon Reinforcement Learning](https://mlsanity.com/paper/2002.04518/) (2020)
- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [Causal Effect Inference for Structured Treatments](https://mlsanity.com/paper/2106.01939/) (2021)
- [The Sensitivity of Counterfactual Fairness to Unmeasured Confounding](https://mlsanity.com/paper/1907.01040/) (2019)
- [A Class of Algorithms for General Instrumental Variable Models](https://mlsanity.com/paper/2006.06366/) (2020)
- [Flexible sensitivity analysis for observational studies without observable implications](https://mlsanity.com/paper/1809.00399/) (2018)
- [How and Why to Use Experimental Data to Evaluate Methods for Observational Causal Inference](https://mlsanity.com/paper/2010.03051/) (2020)
- [The Inflation Technique for Causal Inference with Latent Variables](https://mlsanity.com/paper/1609.00672/) (2016)

## Built on by (most cited first, 25 of 25)

- [Sharp Bounds for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2305.16988/) (2023)
- [Scalable Sensitivity and Uncertainty Analysis for Causal-Effect Estimates of Continuous-Valued Interventions](https://mlsanity.com/paper/2204.10022/) (2022)
- [Partial Identification of Treatment Effects with Implicit Generative Models](https://mlsanity.com/paper/2210.08139/) (2022)
- [A Neural Framework for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2311.16026/) (2023)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments](https://mlsanity.com/paper/2406.02464/) (2024)
- [Towards Bounding Causal Effects under Markov Equivalence](https://mlsanity.com/paper/2311.07259/) (2023)
- [Partial Identification of Dose Responses with Hidden Confounders](https://mlsanity.com/paper/2204.11206/) (2022)
- [AI for Science: An Emerging Agenda](https://mlsanity.com/paper/2303.04217/) (2023)
- [Consistency of Neural Causal Partial Identification](https://mlsanity.com/paper/2405.15673/) (2024)
- [Sequential Underspecified Instrument Selection for Cause-Effect Estimation](https://mlsanity.com/paper/2302.05684/) (2023)
- [Counterfactual Fairness Is Not Demographic Parity, and Other Observations](https://mlsanity.com/paper/2402.02663/) (2024)
- [Targeted Sequential Indirect Experiment Design](https://mlsanity.com/paper/2405.19985/) (2024)
- [Learning Representations of Instruments for Partial Identification of Treatment Effects](https://mlsanity.com/paper/2410.08976/) (2024)
- [Bounding probabilities of causation through the causal marginal problem](https://mlsanity.com/paper/2304.02023/) (2023)
- [Approximate Causal Effect Identification under Weak Confounding](https://mlsanity.com/paper/2306.13242/) (2023)
- [IV-ICL: Bounding Causal Effects with Instrumental Variables via In-Context Learning](https://mlsanity.com/paper/2605.12924/) (2026)
- [Information-Theoretic Causal Bounds under Unmeasured Confounding](https://mlsanity.com/paper/2601.17160/) (2026)
- [Foundation Models for Partial Causal Identification](https://mlsanity.com/paper/2608.20841/) (2026)
- [Tightening Bounds on Probabilities of Causation By Merging Datasets](https://mlsanity.com/paper/2310.08406/) (2023)
- [Your Assumed DAG is Wrong and Here's How To Deal With It](https://mlsanity.com/paper/2502.17030/) (2025)
- [Assessing the robustness of heterogeneous treatment effects in survival analysis under informative censoring](https://mlsanity.com/paper/2510.13397/) (2025)
- [Bounding Causal Effects with Leaky Instruments](https://mlsanity.com/paper/2404.04446/) (2024)
- [Quantum oracles give an advantage for identifying classical counterfactuals](https://mlsanity.com/paper/2512.13692/) (2025)
- [Causal Variational Deep Embedding: A Family of Interventional Generators for Confounded Images](https://mlsanity.com/paper/2606.21806/) (2026)

## Abstract (arXiv)

Causal effect estimation is important for many tasks in the natural and social sciences. We design algorithms for the continuous partial identification problem: bounding the effects of multivariate, continuous treatments when unmeasured confounding makes identification impossible. Specifically, we cast causal effects as objective functions within a constrained optimization problem, and minimize/maximize these functions to obtain bounds. We combine flexible learning algorithms with Monte Carlo methods to implement a family of solutions under the name of stochastic causal programming. In particular, we show how the generic framework can be efficiently formulated in settings where auxiliary variables are clustered into pre-treatment and post-treatment sets, where no fine-grained causal graph can be easily specified. In these settings, we can avoid the need for fully specifying the distribution family of hidden common causes. Monte Carlo computation is also much simplified, leading to algorithms which are more computationally stable against alternatives.