Comparison theorems on large-margin learning
Comparison theorems on large-margin learning
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DOI：
10.1142/s0219691321500156
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发表时间：
2019-08
期刊：
影响因子：
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通讯作者：
Jun Fan;Daohong Xiang
中科院分区：
文献类型：
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作者：
Jun Fan;Daohong Xiang
本文研究了与一类称为大边际统一机（LUMS）的Lipschitz凸损失函数相关的二进制分类问题，该问题在基于分布的似然方法和基于边际的方法之间架起了一座天然的桥梁。LUM可以克服支持向量机在高维低样本情况下的数据堆积问题，但从学习理论的角度对其进行理论分析还很缺乏。在本文中，我们建立了一些新的比较定理的所有LUM损失函数，发挥了关键作用的误差分析的大间隔学习算法。基于所得到的比较定理，我们进一步推导出与不同高斯核相关的正则化LUMS方案的学习率，这可能是独立的兴趣。
This paper studies the binary classification problem associated with a family of Lipschitz convex loss functions called large-margin unified machines (LUMs), which offers a natural bridge between distribution-based likelihood approaches and margin-based approaches. LUMs can overcome the so-called data piling issue of support vector machine in the high-dimension and low-sample size setting, while their theoretical analysis from the perspective of learning theory is still lacking. In this paper, we establish some new comparison theorems for all LUM loss functions which play a key role in the error analysis of large-margin learning algorithms. Based on the obtained comparison theorems, we further derive learning rates for regularized LUMs schemes associated with varying Gaussian kernels, which maybe of independent interest.