  Quantifying uncertainty in model predictions is a common goal for
practitioners seeking more than just point predictions. One tool for
uncertainty quantification that requires minimal assumptions is conformal
inference, which can help create probabilistically valid prediction regions for
black box models. Classical conformal prediction only provides marginal
validity, whereas in many situations locally valid prediction regions are
desirable. Deciding how best to partition the feature space X when applying
localized conformal prediction is still an open question. We present MD-split+,
a practical local conformal approach that creates X partitions based on
localized model performance of conditional density estimation models. Our
method handles complex real-world data settings where such models may be
misspecified, and scales to high-dimensional inputs. We discuss how our local
partitions philosophically align with expected behavior from an unattainable
conditional conformal inference approach. We also empirically compare our
method against other local conformal approaches.
