🤖 AI Summary
Causal inference often relies on strong, unverifiable assumptions—such as no unmeasured confounding and perfect compliance—leading to unreliable effect estimates. This paper systematically investigates bounding causal effects and counterfactual queries (e.g., the probability of necessity and sufficiency, PNS) under partial identification. We extend entropy-constrained methods for the first time to bound necessity and sufficiency probabilities, and develop a unified evaluation framework integrating symbolic reasoning, optimization, and information theory. We propose a decision-tree– and machine-learning–guided algorithm selection strategy, validated through large-scale discrete and continuous simulations (thousands of runs) assessing tightness, computational efficiency, and robustness of bounds. We release CausalBoundingEngine, an open-source Python toolkit enabling integrated invocation and comparative benchmarking of multiple bounding methods. Our approach significantly enhances the reliability and practicality of causal inference under realistic, non-ideal conditions.
📝 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.