论文标题
在繁殖核孔隙空间中的正则最小二乘分析
Analysis of Regularized Least Squares in Reproducing Kernel Krein Spaces
论文作者
论文摘要
在本文中，我们研究了繁殖核孔隙空间（RKKS）中无限核的正则最小二乘的渐近特性。通过将有界的超球限制引入此类非凸正同行风险最小化问题，我们从理论上证明，该问题具有在球体上具有封闭形式的全球最佳解决方案，这使得RKK中的近似值分析可行。关于不确定的内部产品引起的原始正规化学剂，我们修改了传统的误差分解技术，根据基于矩阵扰动理论的引入的假设误差证明了收敛结果，并得出了RKKS中这种正则回归问题的学习率。在某些情况下，RKK中的派生学习率与重现核Hilbert Spaces（RKHS）的学习率相同，这实际上是RKKS中正规化学习算法的近似分析的第一项工作。
In this paper, we study the asymptotic properties of regularized least squares with indefinite kernels in reproducing kernel Krein spaces (RKKS). By introducing a bounded hyper-sphere constraint to such non-convex regularized risk minimization problem, we theoretically demonstrate that this problem has a globally optimal solution with a closed form on the sphere, which makes approximation analysis feasible in RKKS. Regarding to the original regularizer induced by the indefinite inner product, we modify traditional error decomposition techniques, prove convergence results for the introduced hypothesis error based on matrix perturbation theory, and derive learning rates of such regularized regression problem in RKKS. Under some conditions, the derived learning rates in RKKS are the same as that in reproducing kernel Hilbert spaces (RKHS), which is actually the first work on approximation analysis of regularized learning algorithms in RKKS.
