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Non-Asymptotic Analysis of -Norm Support Vector Machines

机译:-范数支持向量机的非渐近分析

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Support vector machines (SVMs) with the -penalty became a standard tool in the analysis of high-dimensional classification problems with sparsity constraints in many applications, including bioinformatics and signal processing. We give non-asymptotic results on the performance of -SVM in identification of sparse classifiers. We show that an -dimensional -sparse classification vector can be (with high probability) well approximated from only Gaussian trials. We derive similar estimates also in the presence of misclassifications and for the so-called doubly regularized SVM, which combines the - and the -penalty. Similar bounds were obtained earlier in the analysis of LASSO and 1-Bit compressed sensing.
机译:具有-penalty的支持向量机(SVM)成为分析在许多应用中具有稀疏性约束的高维分类问题的标准工具,包括生物信息学和信号处理。我们给出了-SVM在稀疏分类器识别中的性能的非渐近结果。我们表明,仅高斯试验可以很好地近似三维稀疏分类向量。在存在错误分类的情况下,对于结合了-和-惩罚的所谓的双正则SVM,我们也得出了类似的估计。在分析LASSO和1位压缩感测时,已经获得了相似的界限。

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