  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.
