In Machine Learning (ML), a regression algorithm aims to minimize a loss function based on data. An assessment method in this context seeks to quantify the discrepancy between the optimal response for an input-output system and the estimate produced by a learned predictive model (the student). Evaluating the quality of a learned regressor remains challenging without access to the true data-generating mechanism, as no data-driven assessment method can ensure the achievability of global optimality. This work introduces the Information Teacher, a novel data-driven framework for evaluating regression algorithms with formal performance guarantees to assess global optimality. Our novel approach builds on estimating the Shannon mutual information (MI) between the input variables and the residuals and applies to a broad class of additive noise models. Through numerical experiments, we confirm that the Information Teacher is capable of detecting global optimality, which is aligned with the condition of zero estimation error with respect to the -- inaccessible, in practice -- true model, working as a surrogate measure of the ground truth assessment loss and offering a principled alternative to conventional empirical performance metrics.

翻译：在机器学习（ML）中，回归算法的目标是最小化基于数据的损失函数。在此背景下，一种评估方法旨在量化输入-输出系统的最优响应与学习得到的预测模型（学生模型）所产生的估计之间的差异。由于无法获知真实的数据生成机制，且没有任何数据驱动的评估方法能够确保全局最优性的可达性，评估学习得到的回归器的质量仍然具有挑战性。本文引入了信息教师（Information Teacher），这是一种新颖的数据驱动框架，用于评估回归算法，并提供形式化的性能保证以评估全局最优性。我们的新方法建立在估计输入变量与残差之间的香农互信息（MI）的基础上，并适用于一大类加性噪声模型。通过数值实验，我们证实信息教师能够检测全局最优性，这与相对于（实践中无法访问的）真实模型的零估计误差条件相一致，可作为真实评估损失的替代度量，并为传统的经验性能指标提供了一种有原则的替代方案。