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arXiv 1605.00751cs.LG
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从具有实例相关损坏的二进制标签中学习

Learning from Binary Labels with Instance-Dependent Corruption

Data61;Australian National University(澳大利亚国立大学);Queensland University of Technology(昆士兰科技大学);Microsoft Research Bangalore(微软研究院班加罗尔分院)

Aditya Krishna Menon, Brendan van Rooyen, Nagarajan Natarajan

摘要:

假设我们有一个实例样本,这些实例与被任意实例和标签相关噪声破坏的二进制标签配对。有了足够多的这样的样本,我们是否可以根据无噪声分布对实例进行最佳分类和排名?我们提供了一个理论分析这个问题,有三个主要贡献。首先,我们证明,对于依赖于实例的噪声,任何算法,是一致的分类上的噪声分布也是一致的清洁分布。其次,我们证明了,对于广泛的一类实例和标签相关的噪声,一个类似的一致性结果适用于ROC曲线下的面积。第三,对于后一种噪声模型,当无噪声类概率函数属于广义线性模型家族时,我们证明了Isotron可以有效地和可证明地从损坏的样本中学习。

英文摘要:

Suppose we have a sample of instances paired with binary labels corrupted by arbitrary instance- and label-dependent noise. With sufficiently many such samples, can we optimally classify and rank instances with respect to the noise-free distribution? We provide a theoretical analysis of this question, with three main contributions. First, we prove that for instance-dependent noise, any algorithm that is consistent for classification on the noisy distribution is also consistent on the clean distribution. Second, we prove that for a broad class of instance- and label-dependent noise, a similar consistency result holds for the area under the ROC curve. Third, for the latter noise model, when the noise-free class-probability function belongs to the generalised linear model family, we show that the Isotron can efficiently and provably learn from the corrupted sample.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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