Conformalized Kernel Ridge Regression and its Efficiency

Dr. Evgeny Burnaev (speaker)
Russia, Institute for Information Transmission Problems of Russian Academy of Sciences
Prof. Vladimir Vovk
UK, Royal Holloway, University of London
Conformal prediction is a method of producing prediction sets that can be applied on top of a wide range of prediction algorithms. The method has a guaranteed coverage probability under the standard IID assumption regardless of whether the assumptions (often considerably more restrictive) of the underlying algorithm are satisfied. However, for the method to be really useful it is desirable that in the case where the assumptions of the underlying algorithm are satisfied, the conformal predictor loses little in efficiency as compared with the underlying algorithm (whereas being a conformal predictor, it has a stronger guarantee of validity). In this paper we explore the degree to which this additional requirement of efficiency is satisfied in the case of Bayesian kernel ridge regression; we find that asymptotically conformal prediction sets differ little from kernel ridge regression prediction intervals when the standard Bayesian assumptions are satisfied.