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Estimation in Reproducing Kernel Hilbert Spaces With Dependent Data
IEEE Transactions on Information Theory ( IF 2.5 ) Pub Date : 2020-12-16 , DOI: 10.1109/tit.2020.3045290
Alessio Sancetta

This paper derives consistency results for estimation in the finite direct sum of reproducing kernel Hilbert spaces (RKHS) for dependent data. The link between penalized and constrained estimation is established. We consider the relation between topological equivalent norms for direct sums of RKHS. These norms have different implications for estimation. Estimation in a ball of the RKHS defined by these norms essentially results in estimation with a ridge and Lasso penalty, respectively. A greedy algorithm for the solution of the estimation problem under these two norms is discussed for general loss functions.

中文翻译:

用相关数据重现内核希尔伯特空间的估计

本文导出了一致性结果,用于在相关数据的再生内核希尔伯特空间(RKHS)的有限直接总和中进行估算。建立了惩罚估计与约束估计之间的联系。我们考虑RKHS直接和的拓扑等效规范之间的关系。这些规范对估计有不同的含义。由这些准则定义的RKHS球的估计实质上导致分别以岭和套索罚分进行估计。针对一般损失函数,讨论了在这两个范数下求解估计问题的贪心算法。
更新日期:2021-02-19
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