Learning theory estimates for coefficient-based regularized regression
Learning theory estimates for coefficient-based regularized regression
复制标题
基于系数的正则回归的学习理论估计
DOI：
10.1016/j.acha.2012.05.001
复制
发表时间：
2013-03-01
影响因子：
2.5
通讯作者：
Shi, Lei
中科院分区：
文献类型：
--
作者：
Shi, Lei
我们考虑了数据依赖假设空间中基于系数的正则化回归。对于给定的样本集合，该假设空间中的函数被定义为由核函数和样本数据生成的基函数的线性组合。我们不需要核是对称的或半正定的，这为学习算法提供了灵活性和自适应性。该算法的另一个优点是，它是计算有效的，没有任何优化过程。在本文中，我们应用浓度技术与l（2）-经验覆盖数，提出了一个详细的容量依赖分析的算法，它产生成形估计的置信估计和收敛速度。当核是C-无穷大时，在回归函数的一个非常温和的正则性条件下，速率可以任意接近m（-1）。(C)2012 Elsevier Inc. All rights reserved.
We consider a coefficient-based regularized regression in a data dependent hypothesis space. For a given set of samples, functions in this hypothesis space are defined to be linear combinations of basis functions generated by a kernel function and sample data. We do not need the kernel to be symmetric or positive semi-definite, which provides flexibility and adaptivity for the learning algorithm. Another advantage of this algorithm is that, it is computationally effective without any optimization processes. In this paper, we apply concentration techniques with l(2)-empirical covering numbers to present an elaborate capacity dependent analysis for the algorithm, which yields shaper estimates in both confidence estimation and convergence rate. When the kernel is C-infinity, under a very mild regularity condition on the regression function, the rate can be arbitrarily close to m(-1). (C) 2012 Elsevier Inc. All rights reserved.