Conformal prediction (CP) quantifies the uncertainty of machine learning models by constructing sets of observable outputs. These sets are constructed by assigning a so-called consensus score, a value calculated using the input point of interest, the prediction model, and previous observations. CP sets are then obtained by evaluating the consensus score of all possible outcomes, and selecting them according to their score. Because of this level step, most CP methods rely on fixed point functions. The challenge in extrapolating these points to different spaces is that there is no canonical order of vectors. To address this, we use a natural extension of the multivariate outcome measure based on optimal transport (OT). Our method, OTCP, provides a systematic framework for constructing consistent prediction sets in multidimensional settings, preserving free coverage guarantees with finite data samples. We demonstrate tangible benefits on a benchmark dataset for multivariate regression problems and address the computational and statistical trade-offs that arise when estimating consensus scores with OT maps.
