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Unified Sharp Bounds on Probabilities of Causation — arXiv:2610.27398

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.27398
License (as archived): CC0-1.0
Archived: 2026-10-21T07:06:31.702Z
SHA-256 of the archived text: 0c2e64604e708c27f3c44b5cc78dbb21113f5de4a5a50b01eadc4bc12e5e140b
Stable URL of this page: https://metraipolis.com/documento/dc_2f2f45f9fa3f

How to cite

Unified Sharp Bounds on Probabilities of Causation — arXiv:2610.27398 — arXiv (en), https://arxiv.org/abs/2610.27398 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2f2f45f9fa3f (Metraipolis archive dc_2f2f45f9fa3f, sha256 0c2e64604e708c27f3c44b5cc78dbb21113f5de4a5a50b01eadc4bc12e5e140b)

BibTeX

@misc{dc2f2f45f9fa3f,
  title = {Unified Sharp Bounds on Probabilities of Causation — arXiv:2610.27398},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.27398},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2f2f45f9fa3f; sha256 0c2e64604e708c27f3c44b5cc78dbb21113f5de4a5a50b01eadc4bc12e5e140b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.27398. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Probabilities of causation (PoCs) have developed steadily, from the binary measures first introduced by Pearl to the non-binary setting recently studied by Shu et al. As the theory has matured, PoCs have found applications in a growing range of areas, including personalized medicine, marketing and legal attribution. Shu et al. proposed closed-form bounds for multi-valued treatments and outcomes and proved them valid, but left their sharpness in high dimensions open. We close this gap with a mathematical proof. We further show that $\PNS$, $\PSub$, $\PRep$ and $\PN$ are all special cases of a single, more general formula. Combined with their equivalence classes, this settles the question of sharp bounds for discrete PoCs from experimental and observational data: in every dimension, they are given in closed form by a single theorem.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.AI, nuovi lavori del giorno).
Categorie arXiv: Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2610.27398 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-21T07:05:43.405Z dalla pagina https://arxiv.org/list/cs.AI/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).