Gandharv Patil, Keyi Tang, Raquel Aoki, Leo Guelman
arXiv 8 May 2026 · Statistics — Machine Learning
arXiv:2605.07065 · PDF · DOI · OpenAlex · Extracted main text
Individual treatment effects are not point-identified from data. The Probability of Necessity and Sufficiency (PNS) circumvents this limitation by characterizing individual-level causality through intersection bounds derived from combined experimental and observational data. In finite samples, however, standard plug-in estimators systematically fail: they violate structural probability constraints and suffer from extremum bias induced by max-min operators, yielding spuriously narrow intervals. We propose a neural framework for finite-sample PNS estimation that resolves both pathologies. We introduce an anchored neural architecture that guarantees structural constraint satisfaction by construction. To correct extremum bias, we employ precision-corrected intersection-bound inference, leveraging Epistemic Neural Networks for scalable, high-dimensional uncertainty quantification. Empirical evaluations confirm that this approach maintains nominal coverage and exact constraint validity in high-dimensional regimes where standard estimators systematically undercover.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| osband2023epistemic | unmatched citation key osband2023epistemic | 0.928 | 5 | 3 | 80% |
| 2 | Tian, Jin and Pearl, Judea (2000) Probabilities of Causation: Bounds and Identification | 0.830 | 7 | 5 | 57% |
| 3 | Chernozhukov, Victor and Lee, Sokbae and Rosen, Adam M (2013) Intersection Bounds: Estimation and Inference | 0.773 | 13 | 5 | 46% |
| 4 | Li, Ang and Mao, Ruirui and Pearl, Judea (2022) Probabilities of Causation: Adequate Size of Experimental and Observational Samples | 0.511 | 3 | 2 | 33% |
| 5 | ACIC (2019) ACIC 2019 Data Challenge Datasets | 0.405 | 1 | 1 | 100% |
| 6 | Charpentier, Bertrand and Zügner, Daniel and Günnemann, Stephan (2020) Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts | 0.405 | 1 | 1 | 100% |
| 7 | Jacot, Arthur and Gabriel, Franck and Hongler, Clément (2018) Neural Tangent Kernel: Convergence and Generalization in Neural Networks | 0.405 | 1 | 1 | 100% |
| 8 | Kawakami, Yuta and Kuroki, Manabu and Tian, Jin (2024) Probabilities of Causation for Continuous and Vector Variables | 0.405 | 1 | 1 | 100% |
| 9 | Li, Ang and Pearl, Judea (2024) Probabilities of Causation with Nonbinary Treatment and Effect | 0.405 | 1 | 1 | 100% |
| 10 | Osband, Ian and Aslanides, John and Cassirer, Albin (2018) Randomized Prior Functions for Deep Reinforcement Learning | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 37 scored citations. 1 of these could not be matched to a bibliography entry, so only the citation key is shown.