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arXiv 1901.09503stat.MLcs.LG
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基于加权积分概率距离的正向无标记学习的原理分析分类器

Principled analytic classifier for positive-unlabeled learning via weighted integral probability metric

Center for Advanced Intelligence Project, RIKEN(理化学研究所先进智能项目中心);Graduate School of Frontier Sciences, The University of Tokyo(东京大学前沿科学研究生院);Department of Statistics, Seoul National University(首尔国立大学统计系)

Yongchan Kwon, Wonyoung Kim, Masashi Sugiyama, Myunghee Cho Paik

摘要:

我们考虑只从正的和未标记的观察学习二元分类器的问题(称为PU学习)。PU学习的最新研究在理论和经验上都显示出优越的性能。然而,大多数现有的算法可能不适合大规模数据集,因为它们面临着一个大的Gram矩阵的重复计算或需要大量的超参数优化。在本文中,我们提出了一个计算效率和理论基础PU学习算法。当假设空间是再生核希尔伯特空间中的闭球时,所提出的PU学习算法产生封闭形式的分类器。此外,我们建立了估计误差和超额风险的上界。所得到的估计误差界比已有的结果更尖锐,并且所得到的超额风险界具有显式形式,且随着样本量的增加而消失。最后,我们使用合成和真实数据集进行了大量的数值实验,证明了所提出的算法的准确性,可扩展性和鲁棒性。

英文摘要:

We consider the problem of learning a binary classifier from only positive and unlabeled observations (called PU learning). Recent studies in PU learning have shown superior performance theoretically and empirically. However, most existing algorithms may not be suitable for large-scale datasets because they face repeated computations of a large Gram matrix or require massive hyperparameter optimization. In this paper, we propose a computationally efficient and theoretically grounded PU learning algorithm. The proposed PU learning algorithm produces a closed-form classifier when the hypothesis space is a closed ball in reproducing kernel Hilbert space. In addition, we establish upper bounds of the estimation error and the excess risk. The obtained estimation error bound is sharper than existing results and the derived excess risk bound has an explicit form, which vanishes as sample sizes increase. Finally, we conduct extensive numerical experiments using both synthetic and real datasets, demonstrating improved accuracy, scalability, and robustness of the proposed algorithm.

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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