In this paper I propose a generative model of supervised learning that unifies two approaches to supervised learning, using a concept of a correct loss function. Addressing two measurability problems, which have been ignored in statistical learning theory, I propose to use convergence in outer probability to characterize the consistency of a learning algorithm. Building upon these results, I extend a result due to Cucker-Smale, which addresses the learnability of a regression model, to the setting of a conditional probability estimation problem. Additionally, I present a variant of Vapnik-Stefanuyk's regularization method for solving stochastic ill-posed problems, and using it to prove the generalizability of overparameterized supervised learning models.

翻译：本文提出了一种基于正确损失函数概念的监督学习生成模型，该模型统一了两种监督学习方法。针对统计学习理论中已被忽略的两个可测性问题，我提出使用外概率收敛来刻画学习算法的一致性。基于上述结果，我将Cucker-Smale关于回归模型可学习性的经典结论推广至条件概率估计问题框架。此外，本文提出了Vapnik-Stefanyuk随机不适定问题正则化方法的一种变体，并利用该方法证明了过参数化监督学习模型的泛化能力。