Estimating Probabilities of Causation with Machine Learning Models

Probabilities of causation play a crucial role in modern decision-making. This paper addresses the challenge of predicting probabilities of causation for subpopulations with insufficient data using machine learning models. Tian and Pearl first defined and derived tight bounds for three fundamental probabilities of causation: the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of necessity (PN). However, estimating these probabilities requires both experimental and observational distributions specific to each subpopulation, which are often unavailable or impractical to obtain with limited population-level data. We assume that the probabilities of causation for each subpopulation are determined by its characteristics. To estimate these probabilities for subpopulations with insufficient data, we propose using machine learning models that draw insights from subpopulations with sufficient data. Our evaluation of multiple machine learning models indicates that, given sufficient population-level data and an appropriate choice of machine learning model and activation function, PNS can be effectively predicted. Through simulation studies, we show that our multilayer perceptron (MLP) model with the Mish activation function achieves a mean absolute error (MAE) of approximately 0.02 in predicting PNS for 32,768 subpopulations using data from around 2,000 subpopulations.