Efficiency of conformalized ridge regression
This work addresses the efficiency concern for practitioners using conformal prediction with ridge regression, showing it is incremental in validating minimal loss under ideal conditions.
The paper investigates the efficiency of conformal prediction when applied to Bayesian ridge regression, finding that asymptotically, the conformal prediction sets differ little from ridge regression prediction intervals under standard Bayesian assumptions.
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 the 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 ridge regression; we find that asymptotically conformal prediction sets differ little from ridge regression prediction intervals when the standard Bayesian assumptions are satisfied.