论文标题
希尔伯特秤中的逆学习
Inverse learning in Hilbert scales
论文作者
论文摘要
我们在统计学习环境中研究了与嘈杂数据的线性逆问题。通过希尔伯特量表的一般正则化方案寻求随机噪声数据的大致重建。我们在先前的假设和一定的链接条件下讨论正规化解决方案的收敛速率。我们以某些距离函数来表达错误。对于具有源条件下给出的平滑度的回归函数，可以明确建立界限。
We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regularization schemes in Hilbert scale. We discuss the rates of convergence for the regularized solution under the prior assumptions and a certain link condition. We express the error in terms of certain distance functions. For regression functions with smoothness given in terms of source conditions the error bound can then be explicitly established.
