Symbolic Regression of Confidence Intervals for Conformal Prediction

Abstract

Conformal prediction is a class of algorithms designed to deliver confidence intervals around point predictions of models, with robust theoretical guarantees. Nevertheless, when dealing with regression problems, the original methodology always computes confidence intervals of the same size, independently of the magnitude of the predicted value y^, impairing the potential usefulness of the information. Several alternatives to properly scale the confidence intervals have been proposed in specialized literature, using assessments of the difficulty of predictions to produce wider intervals for more difficult points and tighter ones for easier predictions. However, each conformal prediction algorithm only exploits one specific type of information to evaluate the difficulty of a point prediction, such as Euclidean distance from points observed during training, or variance in the values of predictions for neighboring points. In this work, we introduce a novel symbolic regression approach to computation of confidence intervals. The algorithm can take into account all types of information considered by other conformal predictors at the same time, delivering human-interpretable equations that describe the amplitude of the intervals, tailored to the specific regression problem under evaluation. Experimental results show that the proposed approach outperforms other conformal predictors on an established benchmark suite of regression problems.