Cross-Validation with Confidence
This addresses model selection reliability for statisticians and machine learning practitioners, offering a principled improvement over existing cross-validation methods.
The paper tackles the problem of traditional cross-validation selecting overfitting models by developing a new method that accounts for testing sample uncertainty, outputting a set of candidate models containing the best one with guaranteed probability and achieving consistent variable selection in linear regression.
Cross-validation is one of the most popular model selection methods in statistics and machine learning. Despite its wide applicability, traditional cross validation methods tend to select overfitting models, due to the ignorance of the uncertainty in the testing sample. We develop a new, statistically principled inference tool based on cross-validation that takes into account the uncertainty in the testing sample. This new method outputs a set of highly competitive candidate models containing the best one with guaranteed probability. As a consequence, our method can achieve consistent variable selection in a classical linear regression setting, for which existing cross-validation methods require unconventional split ratios. When used for regularizing tuning parameter selection, the method can provide a further trade-off between prediction accuracy and model interpretability. We demonstrate the performance of the proposed method in several simulated and real data examples.