Least-squares regularized regression with dependent samples and q-penalty
Least-squares regularized regression with dependent samples and q-penalty
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DOI：
10.1080/00036811.2011.559465
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发表时间：
2012-05
影响因子：
1.1
通讯作者：
Yunlong Feng
中科院分区：
文献类型：
--
作者：
Yunlong Feng
当采样过程是独立的并且正则化项是再生核希尔伯特空间（RKHS）中范数的平方时，用于回归的最小二乘正则化学习算法在文献中得到了充分研究。还对相关采样过程或正则化器进行了一些分析，即函数范数（q 惩罚）的 q 次方（0 < q ≤ 2）。本文的目的是当采样序列弱依赖满足指数衰减 α 混合条件时以及正则化器采用 0 < q ≤ 2 的 q 惩罚时，对最小二乘正则化回归算法进行误差分析。我们使用覆盖数参数并根据α-混合衰减、近似条件和 RKHS 球的容量。
Least-squares regularized learning algorithms for regression were well-studied in the literature when the sampling process is independent and the regularization term is the square of the norm in a reproducing kernel Hilbert space (RKHS). Some analysis has also been done for dependent sampling processes or regularizers being the qth power of the function norm (q-penalty) with 0 < q ≤ 2. The purpose of this article is to conduct error analysis of the least-squares regularized regression algorithm when the sampling sequence is weakly dependent satisfying an exponentially decaying α-mixing condition and when the regularizer takes the q-penalty with 0 < q ≤ 2. We use a covering number argument and derive learning rates in terms of the α-mixing decay, an approximation condition and the capacity of balls of the RKHS.