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The field of distribution-free predictive inference provides tools forprovably valid prediction without any assumptions on the distribution of thedata, which can be paired with any regression algorithm to provide accurate andreliable predictive intervals. The guarantees provided by these methods aretypically marginal, meaning that predictive accuracy holds on average over boththe training data set and the test point that is queried. However, it may bepreferable to obtain a stronger guarantee of training-conditional coverage,which would ensure that most draws of the training data set result in accuratepredictive accuracy on future test points. This property is known to hold forthe split conformal prediction method. In this work, we examine thetraining-conditional coverage properties of several other distribution-freepredictive inference methods, and find that training-conditional coverage isachieved by some methods but is impossible to guarantee without furtherassumptions for others.

Training-conditional coverage for distribution-free predictive inference