Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates, require complete causal graphs, or rely on restrictive binary settings, limiting their practical use. In real-world applications, causal information is often partial but nontrivial. This paper proposes a general framework for bounding probabilities of causation using partial causal information. We show how the available structural or statistical information can be systematically incorporated as constraints in a optimization programming formulation, yielding tighter and formally valid bounds without full identifiability. This approach extends the applicability of probabilities of causation to realistic settings where causal knowledge is incomplete but informative.
General sample size analysis for probabilities of causation: a delta method approach
Department of Statistics, Florida State University（佛罗里达州立大学统计学系）；Department of Computer Science, Cornell University（康奈尔大学计算机科学系）；Department of Computer Science, University of California Los Angeles（美国加州大学洛杉矶分校计算机科学系）；Department of Computer Science, Florida State University（佛罗里达州立大学计算机科学系）
Partial Identification under Causal Orders by Linear Programming
Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA)（达勒·莫勒人工智能研究所）；Scuola Universitaria Professionale della Svizzera Italiana (SUPSI)（瑞士意大利语区应用科技大学）
