Consistency and Convergence Rates of One-Class SVMs and Related Algorithms
Consistency and Convergence Rates of One-Class SVMs and Related Algorithms
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发表时间：
2006-12
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通讯作者：
Régis Vert;Jean-Philippe Vert
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作者：
Régis Vert;Jean-Philippe Vert
我们确定的支持向量机（SVM）和相关算法，最小化的正则化的经验凸损失函数的高斯RBF核的再生核希尔伯特空间中计算的函数的渐近行为，在例子的数量趋于无穷大的情况下，高斯核的带宽趋于0，和正则化参数保持固定。在L2意义上的非渐近收敛界限，这一限制，连同上界的分类错误，收敛到贝叶斯风险，因此证明贝叶斯一致性的各种方法，虽然正规化项不消失。这些结果是特别相关的一类SVM，其中的正则化不能消失的建设，这是第一次被证明是一个一致的密度水平集估计。
We determine the asymptotic behaviour of the function computed by support vector machines (SVM) and related algorithms that minimize a regularized empirical convex loss function in the reproducing kernel Hilbert space of the Gaussian RBF kernel, in the situation where the number of examples tends to infinity, the bandwidth of the Gaussian kernel tends to 0, and the regularization parameter is held fixed. Non-asymptotic convergence bounds to this limit in the L2 sense are provided, together with upper bounds on the classification error that is shown to converge to the Bayes risk, therefore proving the Bayes-consistency of a variety of methods although the regularization term does not vanish. These results are particularly relevant to the one-class SVM, for which the regularization can not vanish by construction, and which is shown for the first time to be a consistent density level set estimator.