Confidence Interval Estimation of Predictive Performance in the Context of AutoML

Any supervised machine learning analysis is required to provide an estimate of the out-of-sample predictive performance. However, it is imperative to also provide a quantification of the uncertainty of this performance in the form of a confidence or credible interval (CI) and not just a point estimate. In an AutoML setting, estimating the CI is challenging due to the ``winner's curse", i.e., the bias of estimation due to cross-validating several machine learning pipelines and selecting the winning one. In this work, we perform a comparative evaluation of 9 state-of-the-art methods and variants in CI estimation in an AutoML setting on a corpus of real and simulated datasets. The methods are compared in terms of inclusion percentage (does a 95\% CI include the true performance at least 95\% of the time), CI tightness (tighter CIs are preferable as being more informative), and execution time. The evaluation is the first one that covers most, if not all, such methods and extends previous work to imbalanced and small-sample tasks. In addition, we present a variant, called BBC-F, of an existing method (the Bootstrap Bias Correction, or BBC) that maintains the statistical properties of the BBC but is more computationally efficient. The results support that BBC-F and BBC dominate the other methods in all metrics measured.