One of the key objects of binary classification is the regression function,
i.e., the conditional expectation of the class labels given the inputs. With
the regression function not only a Bayes optimal classifier can be defined, but
it also encodes the corresponding misclassification probabilities. The paper
presents a resampling framework to construct exact, distribution-free and
non-asymptotically guaranteed confidence regions for the true regression
function for any user-chosen confidence level. Then, specific algorithms are
suggested to demonstrate the framework. It is proved that the constructed
confidence regions are strongly consistent, that is, any false model is
excluded in the long run with probability one. The exclusion is quantified with
probably approximately correct type bounds, as well. Finally, the algorithms
are validated via numerical experiments, and the methods are compared to
approximate asymptotic confidence ellipsoids.

该论文介绍了一个重新采样框架，用于构建精确、无分布偏差且非渐近保证的真实回归函数置信区间，以适应用户选择的信赖水平，并提出了具体算法以演示该框架。通过数值实验验证了算法，并将其与近似渐近保证的置信椭球进行比较。