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Quantifying uncertainty in model predictions is a common goal forpractitioners seeking more than just point predictions. One tool foruncertainty quantification that requires minimal assumptions is conformalinference, which can help create probabilistically valid prediction regions forblack box models. Classical conformal prediction only provides marginalvalidity, whereas in many situations locally valid prediction regions aredesirable. Deciding how best to partition the feature space X when applyinglocalized conformal prediction is still an open question. We present MD-split+,a practical local conformal approach that creates X partitions based onlocalized model performance of conditional density estimation models. Ourmethod handles complex real-world data settings where such models may bemisspecified, and scales to high-dimensional inputs. We discuss how our localpartitions philosophically align with expected behavior from an unattainableconditional conformal inference approach. We also empirically compare ourmethod against other local conformal approaches.

MD-split+: Practical Local Conformal Inference in High Dimensions