Optimal Rates for Regularization Operators in Learning Theory
Optimal Rates for Regularization Operators in Learning Theory
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DOI：
10.21236/ada456685
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发表时间：
2006-09
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影响因子：
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通讯作者：
A. Caponnetto
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文献类型：
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作者：
A. Caponnetto
翻译后摘要：我们开发了一些新的误差界的学习算法引起的正则化方法在回归设置。这个问题的难度的特点是在参数r和s，第一个有关的目标函数的复杂性，第二个连接到输入空间的边际概率测度的有效维数。我们表明，扩展以前的结果，通过适当选择的正则化参数作为可用的例子的数量的函数，它是可能达到最佳的极小极大收敛速度的估计的预期平方损失，在家庭的先验满足约束r + s > 1/2。该设置考虑了标记和未标记的示例，后者对于r < 1/2范围内先验的最优性结果至关重要。
Abstract : We develop some new error bounds for learning algorithms induced by regularization methods in the regression setting. The hardness of the problem is characterized in terms of the parameters r and s, the first related to the complexity of the target function, the second connected to the effective dimension of the marginal probability measure over the input space. We show, extending previous results, that by a suitable choice of the regularization parameter as a function of the number of the available examples, it is possible attain the optimal minimax rates of convergence for the expected squared loss of the estimators, over the family of priors fulfilling the constraint r + s > 1/2. The setting considers both labelled and unlabelled examples, the latter being crucial for the optimality results on the priors in the range r < 1/2 .