Bounding Causal Effects and Counterfactuals

TL;DR

This paper systematically compares and extends various bounding algorithms for causal effect estimation under uncertainty, providing practical tools and guidance for applied causal inference.

Contribution

It unifies and extends state-of-the-art bounding methods, introduces an entropy-based approach for counterfactuals, and offers a practical decision framework and open-source software.

Findings

Extended entropy-bounded method for counterfactuals

Empirical evaluation of bounding algorithms across diverse scenarios

Practical decision tree for method selection and an ML predictor

Abstract

Causal inference often hinges on strong assumptions - such as no unmeasured confounding or perfect compliance - that are rarely satisfied in practice. Partial identification offers a principled alternative: instead of relying on unverifiable assumptions to estimate causal effects precisely, it derives bounds that reflect the uncertainty inherent in the data. Despite its theoretical appeal, partial identification remains underutilized in applied work, in part due to the fragmented nature of existing methods and the lack of practical guidance. This thesis addresses these challenges by systematically comparing a diverse set of bounding algorithms across multiple causal scenarios. We implement, extend, and unify state-of-the-art methods - including symbolic, optimization-based, and information-theoretic approaches - within a common evaluation framework. In particular, we propose an extension of a recently introduced entropy-bounded method, making it applicable to counterfactual queries such as the Probability of Necessity and Sufficiency (PNS). Our empirical study spans thousands of randomized simulations involving both discrete and continuous data-generating processes. We assess each method in terms of bound tightness, computational efficiency, and robustness to assumption violations. To support practitioners, we distill our findings into a practical decision tree for algorithm selection and train a machine learning model to predict the best-performing method based on observable data characteristics. All implementations are released as part of an open-source Python package, CausalBoundingEngine, which enables users to apply and compare bounding methods through a unified interface.