Conformal Multi-Target Hyperrectangles

We propose conformal hyperrectangular prediction regions for multi-target regression. We propose split conformal prediction algorithms for both point and quantile regression to form hyperrectangular prediction regions, which allow for easy marginal interpretation and do not require covariance estimation. In practice, it is preferable that a prediction region is balanced, that is, having identical marginal prediction coverage, since prediction accuracy is generally equally important across components of the response vector. The proposed algorithms possess two desirable properties, namely, tight asymptotic overall nominal coverage as well as asymptotic balance, that is, identical asymptotic marginal coverage, under mild conditions. We then compare our methods to some existing methods on both simulated and real data sets. Our simulation results and real data analysis show that our methods outperform existing methods while achieving the desired nominal coverage and good balance between dimensions.