  Uncertainty quantification of causal effects is crucial for safety-critical
applications such as personalized medicine. A powerful approach for this is
conformal prediction, which has several practical benefits due to
model-agnostic finite-sample guarantees. Yet, existing methods for conformal
prediction of causal effects are limited to binary/discrete treatments and make
highly restrictive assumptions such as known propensity scores. In this work,
we provide a novel conformal prediction method for potential outcomes of
continuous treatments. We account for the additional uncertainty introduced
through propensity estimation so that our conformal prediction intervals are
valid even if the propensity score is unknown. Our contributions are
three-fold: (1) We derive finite-sample prediction intervals for potential
outcomes of continuous treatments. (2) We provide an algorithm for calculating
the derived intervals. (3) We demonstrate the effectiveness of the conformal
prediction intervals in experiments on synthetic and real-world datasets. To
the best of our knowledge, we are the first to propose conformal prediction for
continuous treatments when the propensity score is unknown and must be
estimated from data.
