  We study the problem of learning conditional average treatment effects (CATE)
from high-dimensional, observational data with unobserved confounders.
Unobserved confounders introduce ignorance -- a level of unidentifiability --
about an individual's response to treatment by inducing bias in CATE estimates.
We present a new parametric interval estimator suited for high-dimensional
data, that estimates a range of possible CATE values when given a predefined
bound on the level of hidden confounding. Further, previous interval estimators
do not account for ignorance about the CATE stemming from samples that may be
underrepresented in the original study, or samples that violate the overlap
assumption. Our novel interval estimator also incorporates model uncertainty so
that practitioners can be made aware of out-of-distribution data. We prove that
our estimator converges to tight bounds on CATE when there may be unobserved
confounding, and assess it using semi-synthetic, high-dimensional datasets.
