Probabilities of causation bounds unified across all dimensions
Unified Sharp Bounds on Probabilities of Causation
Artificial Intelligence
Summary
Probabilities of causation help estimate how likely it is that one thing causes another, which is important in medicine, marketing, and law. Previous work found formulas for these probabilities but left some cases unproven, especially when many factors are involved. The authors proved these formulas are exact for every setting, unifying different measures into one general formula. This means we now have clear, reliable bounds for these probabilities no matter how complex the situation.
What this means in practice
- •For personalized medicine teams: Determine exact causal effect bounds for treatments with multiple options, improving treatment decisions based on observed patient data.
- •For legal analytics teams: Precisely estimate causation probabilities for complex evidence scenarios, assisting legal attribution analysis based on both experimental and observational data.
A theory result. No direct application yet.
Authors
Xin Shu, Ang Li
Abstract
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.