Hannes LEEB (Vienna University) – Conditional Predictive Inference for Stable Algorithms
Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 25th September 2023
Hannes LEEB – Conditional Predictive Inference for Stable Algorithms
We investigate generically applicable and intuitively appealing prediction intervals based on k-fold cross-validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training sample (hence, training conditional validity), and show that it is close to the nominal level, in an appropriate sense, provided that the underlying
algorithm used for computing point predictions is sufficiently stable when feature-response pairs are omitted. Our results are based on a finite sample analysis of the empirical distribution function of k-fold cross-validation residuals and hold in nonparametric settings with only minimal assumptions on the error distribution. To illustrate our results, we also apply them to high-dimensional linear predictors, where we obtain uniform asymptotic training conditional validity as both sample size and dimension tend to infinity at the same rate and consistent parameter estimation typically fails. These results show that despite the serious problems of resampling procedures for inference on the unknown parameters, cross-validation methods can be successfully applied to obtain reliable predictive inference
even in high dimensions and conditionally on the training data.
Cristina BUTUCEA (CREST), Alexandre TSYBAKOV (CREST), Karim LOUNICI (CMAP) , Jaouad MOURTADA (CREST)