Probabilities of Causation for Continuous and Vector Variables

TL;DR

This paper extends probabilities of causation to continuous and multivariate variables, providing a comprehensive framework for causal inference in complex scenarios with real-world applications.

Contribution

It introduces new definitions and nonparametric identification theorems for PoC involving continuous, multivariate, and sub-population variables, enhancing causal analysis capabilities.

Findings

Extended PoC to continuous and vector variables

Provided nonparametric identification theorems for new PoC types

Demonstrated application on real-world education data

Abstract

Probabilities of causation (PoC) are valuable concepts for explainable artificial intelligence and practical decision-making. PoC are originally defined for scalar binary variables. In this paper, we extend the concept of PoC to continuous treatment and outcome variables, and further generalize PoC to capture causal effects between multiple treatments and multiple outcomes. In addition, we consider PoC for a sub-population and PoC with multi-hypothetical terms to capture more sophisticated counterfactual information useful for decision-making. We provide a nonparametric identification theorem for each type of PoC we introduce. Finally, we illustrate the application of our results on a real-world dataset about education.