Causal EpiNets: Scalable Inference for Bounds on the Probability of Positive Individual Treatment Effects

Does a treatment help this individual? For binary treatments and outcomes, the Probability of Necessity and Sufficiency (PNS) formalizes this question as the probability of a positive Individual Treatment Effect. In general, PNS is not point identified, but prior work shows that sharp bounds can be obtained by combining randomized and observational data without assuming observational unconfoundedness or positivity. These identification results characterize what can be learned given exact knowledge of the underlying distributions; in practice, however, PNS bounds must be estimated from finite samples. We show that naive plug-in estimation of PNS bounds suffers from two distinct finite-sample pathologies and develop a principled, scalable framework that translates the identification theory into practical estimation with high-dimensional covariates while explicitly addressing both.