Tuning parameters in supervised learning problems are often estimated by cross-validation. The minimum value of the cross-validation error can be biased downward as an estimate of the test error at that same value of the tuning parameter. We propose a simple method for the estimation of this bias that uses information from the cross-validation process. As a result, it requires essentially no additional computation. We apply our bias estimate to a number of popular classifiers in various settings, and examine its performance.
"A bias correction for the minimum error rate in cross-validation." Ann. Appl. Stat. 3 (2) 822 - 829, June 2009. https://doi.org/10.1214/08-AOAS224