Approximate full-conformal multi-task regression with reproducing kernels
This work addresses the challenge of constructing fully conformal prediction regions in multi-task regression, which are typically intractable due to their reliance on an infinite ensemble of predictors. The authors propose a computationally feasible approximation within a vector-valued reproducing kernel Hilbert space, providing theoretical guarantees of achieving the desired coverage level under both known and estimated covariance matrices. In the case of known covariance, they derive an upper bound on the volume of the prediction region and establish its tightness. Empirical evaluations on synthetic data demonstrate that the proposed method substantially outperforms split conformal prediction, yielding significantly smaller prediction regions while maintaining accurate coverage.