  This paper deals with the problem of learning the probabilities of causation
of subpopulations given finite population data. The tight bounds of three basic
probabilities of causation, the probability of necessity and sufficiency (PNS),
the probability of sufficiency (PS), and the probability of necessity (PN),
were derived by Tian and Pearl. However, obtaining the bounds for each
subpopulation requires experimental and observational distributions of each
subpopulation, which is usually impractical to estimate given finite population
data. We propose a machine learning model that helps to learn the bounds of the
probabilities of causation for subpopulations given finite population data. We
further show by a simulated study that the machine learning model is able to
learn the bounds of PNS for 32768 subpopulations with only knowing roughly 500
of them from the finite population data.
