We describe some recent advances in distribution-free prediction intervals in regression, using the conformal inference framework. This framework allows for the construction of a prediction band for the response variable using any estimator of the regression function. The resulting prediction band preserves the consistency properties of the original estimator under standard assumptions, while guaranteeing finite-sample marginal coverage even when these assumptions do not hold. We discuss two major variants of our conformal framework: full conformal inference and split conformal inference, along with a related jackknife method. These methods offer different tradeoffs between statistical accuracy (length of resulting prediction intervals) and computational efficiency. We also develop a new method for constructing valid in-sample prediction intervals called rank-one-out conformal inference, which has essentially the same computational efficiency as split conformal inference. Lastly, if time permits, we will discuss a number of open challenges related to conformal inference.
Much of this represents joint work with my CMU colleagues Jing Lei, Max G’Sell, Alessandro Rinaldo, and Larry Wasserman.