  This paper develops novel conformal methods to test whether a new observation
was sampled from the same distribution as a reference set. Blending inductive
and transductive conformal inference in an innovative way, the described
methods can re-weight standard conformal p-values based on dependent side
information from known out-of-distribution data in a principled way, and can
automatically take advantage of the most powerful model from any collection of
one-class and binary classifiers. The solution can be implemented either
through sample splitting or via a novel transductive cross-validation+ scheme
which may also be useful in other applications of conformal inference, due to
tighter guarantees compared to existing cross-validation approaches. After
studying false discovery rate control and power within a multiple testing
framework with several possible outliers, the proposed solution is shown to
outperform standard conformal p-values through simulations as well as
applications to image recognition and tabular data.
