  Personalized decision making requires the knowledge of potential outcomes
under different treatments, and confidence intervals about the potential
outcomes further enrich this decision-making process and improve its
reliability in high-stakes scenarios. Predicting potential outcomes along with
its uncertainty in a counterfactual world poses the foundamental challenge in
causal inference. Existing methods that construct confidence intervals for
counterfactuals either rely on the assumption of strong ignorability, or need
access to un-identifiable lower and upper bounds that characterize the
difference between observational and interventional distributions. To overcome
these limitations, we first propose a novel approach wTCP-DR based on
transductive weighted conformal prediction, which provides confidence intervals
for counterfactual outcomes with marginal converage guarantees, even under
hidden confounding. With less restrictive assumptions, our approach requires
access to a fraction of interventional data (from randomized controlled trials)
to account for the covariate shift from observational distributoin to
interventional distribution. Theoretical results explicitly demonstrate the
conditions under which our algorithm is strictly advantageous to the naive
method that only uses interventional data. After ensuring valid intervals on
counterfactuals, it is straightforward to construct intervals for individual
treatment effects (ITEs). We demonstrate our method across synthetic and
real-world data, including recommendation systems, to verify the superiority of
our methods compared against state-of-the-art baselines in terms of both
coverage and efficiency
