This article presents a new way to study the theory of regularized learning for generalized data in Banach spaces including representer theorems and convergence theorems. The generalized data are composed of linear functionals and real scalars as the input and output elements to represent the discrete information of different local models. By the extension of the classical machine learning, the empirical risks are computed by the generalized data and the loss functions. According to the techniques of regularization, the exact solutions are approximated globally by minimizing the regularized empirical risks over the Banach spaces. The existence and convergence of the approximate solutions are guaranteed by the relative compactness of the generalized input data in the predual spaces of the Banach spaces.
翻译:本文为研究Banach空间通用数据常规化学习理论,包括代表性理论和趋同理论,提供了一种新的方法。通用数据由线性功能和真实的卡路里组成,作为代表不同地方模型的离散信息的输入和输出要素。通过古典机器学习,经验风险由通用数据和损失功能计算。根据正规化技术,通过尽可能减少Banach空间的常规化经验风险,准确解决方案在全球范围接近。Banach空间前空空空空中通用输入数据的相对紧凑性保证了近似解决方案的存在和趋同性。