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arXiv 2108.09805cs.LGcs.DSstat.ML
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从粗标签中学习的有效算法

Efficient Algorithms for Learning from Coarse Labels

National Technical University of Athens(雅典国家技术大学);University of Wisconsin-Madison(威斯康星大学麦迪逊分校)

Dimitris Fotakis, Alkis Kalavasis, Vasilis Kontonis, Christos Tzamos

摘要:

对于许多学习问题,人们可能无法访问细粒度的标签信息;例如,根据注释者的专业知识,可以将图像标记为哈士奇、狗或甚至动物。在这项工作中,我们正式这些设置和学习的问题,从这样的粗数据。我们观察对应于$\mathcal{Z}$的分区(或分区的混合)的粗略标签,而不是观察来自集合$\mathcal{Z}$的实际标签。我们的主要算法的结果是,基本上任何问题学习细粒度标签也可以有效地学习时,粗数据是足够的信息。我们得到我们的结果,通过一个通用的减少回答细粒度的标签,只有粗糙的标签统计量(SQ)。所需的粗标签的数量多项式地取决于由于粗化引起的信息失真和精细标签的数量$|\mathcal{Z}|$。我们还调查的情况下(无限多)实值标签集中在一个中心问题,在删失和截断统计:高斯平均估计从粗数据。我们提供了一个有效的算法时,分区中的集合是凸的,并建立即使是非常简单的非凸集的问题是NP-难的。

英文摘要:

For many learning problems one may not have access to fine grained label information; e.g., an image can be labeled as husky, dog, or even animal depending on the expertise of the annotator. In this work, we formalize these settings and study the problem of learning from such coarse data. Instead of observing the actual labels from a set $\mathcal{Z}$, we observe coarse labels corresponding to a partition of $\mathcal{Z}$ (or a mixture of partitions). Our main algorithmic result is that essentially any problem learnable from fine grained labels can also be learned efficiently when the coarse data are sufficiently informative. We obtain our result through a generic reduction for answering Statistical Queries (SQ) over fine grained labels given only coarse labels. The number of coarse labels required depends polynomially on the information distortion due to coarsening and the number of fine labels $|\mathcal{Z}|$. We also investigate the case of (infinitely many) real valued labels focusing on a central problem in censored and truncated statistics: Gaussian mean estimation from coarse data. We provide an efficient algorithm when the sets in the partition are convex and establish that the problem is NP-hard even for very simple non-convex sets.

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