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.
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