Generalization error boundaries are essential for comprehending how well machine learning models work. In this work, we suggest a creative method, i.e., the Auxiliary Distribution Method, that derives new upper bounds on generalization errors that are appropriate for supervised learning scenarios. We show that our general upper bounds can be specialized under some conditions to new bounds involving the generalized $\alpha$-Jensen-Shannon, $\alpha$-R\'enyi ($0< \alpha < 1$) information between random variable modeling the set of training samples and another random variable modeling the set of hypotheses. Our upper bounds based on generalized $\alpha$-Jensen-Shannon information are also finite. Additionally, we demonstrate how our auxiliary distribution method can be used to derive the upper bounds on generalization error under the distribution mismatch scenario in supervised learning algorithms, where the distributional mismatch is modeled as $\alpha$-Jensen-Shannon or $\alpha$-R\'enyi ($0< \alpha < 1$) between the distribution of test and training data samples. We also outline the circumstances in which our proposed upper bounds might be tighter than other earlier upper bounds.
翻译:在这项工作中,我们建议一种创新方法,即辅助配送方法,该方法产生适用于监督学习情景的通用错误的新上限。我们表明,我们的一般上限在某些条件下可以专门用于涉及通用的alpha$-Jensen-Shannon、$\alpha$-R\'enyi(0美元 < alpha < 1美元)的通用分配错误界限。在这个工作中,我们建议一种创新方法,即辅助配送方法,该方法产生适用于监督学习情景的通用的通用错误的新的上限。此外,我们证明如何使用我们的辅助配送方法,在监督学习算法的通用分配错误的上限上限值($\alpha$-Jensen-Shannon或$\alpha$-R-enyi(0美元 < < Jensen-alpha < 1美元)之间的随机可变数模型。我们基于通用 $-Jensen-Shannon的信息的上界界限,我们提出的前期测试和上边框中的其他数据可能更加严格。