Title: Some advances in conformal inference

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 new idea to use what we call
"conformalization" of a generic estimator in order to estimate
arbitrary functionals of the conditional distribution of the response
given the predictors.

Much of this represents joint work with my CMU colleagues Jing Lei,
Max G'Sell, Alessandro Rinaldo, and Larry Wasserman.