Post-Selection Confidence Bounds for Prediction Performance

TL;DR

This paper introduces a method to compute valid lower confidence bounds for multiple models selected based on their prediction performance, addressing the challenge of model selection and evaluation in machine learning.

Contribution

It proposes a universal algorithm using bootstrap tilting and maxT correction to provide confidence bounds for multiple models simultaneously, improving reliability especially with small sample sizes.

Findings

Bounds are at least as good as standard methods

Reliably reach nominal coverage probability

Better performance in small sample scenarios

Abstract

In machine learning, the selection of a promising model from a potentially large number of competing models and the assessment of its generalization performance are critical tasks that need careful consideration. Typically, model selection and evaluation are strictly separated endeavors, splitting the sample at hand into a training, validation, and evaluation set, and only compute a single confidence interval for the prediction performance of the final selected model. We however propose an algorithm how to compute valid lower confidence bounds for multiple models that have been selected based on their prediction performances in the evaluation set by interpreting the selection problem as a simultaneous inference problem. We use bootstrap tilting and a maxT-type multiplicity correction. The approach is universally applicable for any combination of prediction models, any model selection strategy, and any prediction performance measure that accepts weights. We conducted various simulation experiments which show that our proposed approach yields lower confidence bounds that are at least comparably good as bounds from standard approaches, and that reliably reach the nominal coverage probability. In addition, especially when sample size is small, our proposed approach yields better performing prediction models than the default selection of only one model for evaluation does.