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Robust Support Vector Machines for Classification with Nonconvex and Smooth Losses

机译：具有非凸和平滑损失的鲁棒支持向量机

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摘要

This letter addresses the robustness problem when learning a large margin classifier in the presence of label noise. In our study, we achieve this purpose by proposing robustified large margin support vector machines. The robustness of the proposed robust support vector classifiers (RSVC), which is interpreted from a weighted viewpoint in this work, is due to the use of nonconvex classification losses. Besides the robustness, we also show that the proposed RSCV is simultaneously smooth, which again benefits from using smooth classification losses. The idea of proposing RSVC comes from M-estimation in statistics since the proposed robust and smooth classification losses can be taken as one-sided cost functions in robust statistics. Its Fisher consistency property and generalization ability are also investigated. Besides the robustness and smoothness, another nice property of RSVC lies in the fact that its solution can be obtained by solving weighted squared hinge loss–based support vector machine problems iteratively. We further show that in each iteration, it is a quadratic programming problem in its dual space and can be solved by using state-of-the-art methods. We thus propose an iteratively reweighted type algorithm and provide a constructive proof of its convergence to a stationary point. Effectiveness of the proposed classifiers is verified on both artificial and real data sets.
机译：这封信解决了在存在标签噪声的情况下学习大型边际分类器时的鲁棒性问题。在我们的研究中，我们通过提出鲁棒的大余量支持向量机来实现此目的。提出的鲁棒支持向量分类器（RSVC）的鲁棒性是从非加权分类损失中得出的，在本文中是从加权观点来解释的。除了鲁棒性，我们还表明，提出的RSCV同时是平滑的，这再次受益于使用平滑的分类损失。提出RSVC的想法来自统计中的M估计，因为建议的鲁棒和平滑分类损失可以视为鲁棒统计中的单方面成本函数。还研究了其Fisher一致性性质和泛化能力。除了鲁棒性和平滑性之外，RSVC的另一个不错的特性是，可以通过迭代解决基于加权平方铰链损耗的支持向量机问题来获得其解决方案。我们进一步证明，在每次迭代中，它在对偶空间中都是一个二次编程问题，可以通过使用最新技术来解决。因此，我们提出了一种迭代重加权类型算法，并提供了其收敛到平稳点的建设性证明。在人工和真实数据集上都验证了提出的分类器的有效性。

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