具有概率态射与核均值嵌入的监督学习
Supervised learning with probabilistic morphisms and kernel mean embeddings
AI总结：
本文提出一种统一两种监督学习方法的生成式模型，利用外概率收敛刻画算法一致性，将 Cucker-Smale 结果扩展至条件概率估计，并提出正则化变体证明过参数化模型的泛化性。
摘要：
本文提出了一种监督学习的生成式模型，通过正确损失函数的概念统一了两种监督学习方法。针对统计学习理论中被忽视的两个可测性问题，提出使用外概率收敛来刻画学习算法的一致性。基于这些结果，将 Cucker-Smale 关于回归模型可学习性的结果扩展至条件概率估计问题的设定中。此外，提出了 Vapnik-Stefanuyk 正则化方法的一种变体以求解随机不适定问题，并用其证明了过参数化监督学习模型的泛化性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
