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arXiv 1602.02450cs.LGstat.ML
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损失因子分解、弱监督学习和标签噪声鲁棒性

Loss factorization, weakly supervised learning and label noise robustness

Australian National University(澳大利亚国立大学);NICTA(国家信息与通信技术研究院);École Polytechnique(巴黎综合理工学院);Sony Computer Science Laboratories Inc.(索尼计算机科学实验室公司);Max Planck Institute for Mathematics in the Sciences(马克斯·普朗克数学与科学研究所)

Giorgio Patrini, Frank Nielsen, Richard Nock, Marcello Carioni

摘要:

我们证明了经验风险的最知名的损失函数因素到一个线性项聚合的所有标签与一个长期的标签是免费的,并可以进一步表示的损失的总和。这甚至适用于非光滑、非凸损失和任何RKHS。第一项是一个(核)平均算子-这项工作的焦点量-我们的特点是标签的充分统计。结果收紧已知的泛化范围,并揭示了新的光对他们的解释。因子分解在弱监督学习中有直接的应用。特别是,我们证明了算法,如SGD和近端方法可以适应以最小的努力来处理弱监督,一旦平均算子估计。我们将这一想法应用于非对称噪声标签的学习,连接和扩展先前的工作。此外,我们发现,大多数损失享有的数据依赖(平均算子)形式的噪声鲁棒性,与已知的负面结果。

英文摘要:

We prove that the empirical risk of most well-known loss functions factors into a linear term aggregating all labels with a term that is label free, and can further be expressed by sums of the loss. This holds true even for non-smooth, non-convex losses and in any RKHS. The first term is a (kernel) mean operator --the focal quantity of this work-- which we characterize as the sufficient statistic for the labels. The result tightens known generalization bounds and sheds new light on their interpretation. Factorization has a direct application on weakly supervised learning. In particular, we demonstrate that algorithms like SGD and proximal methods can be adapted with minimal effort to handle weak supervision, once the mean operator has been estimated. We apply this idea to learning with asymmetric noisy labels, connecting and extending prior work. Furthermore, we show that most losses enjoy a data-dependent (by the mean operator) form of noise robustness, in contrast with known negative results.

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