Electronic Journal of Statistics

Surrogate losses in passive and active learning

Steve Hanneke and Liu Yang

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Active learning is a type of sequential design for supervised machine learning, in which the learning algorithm sequentially requests the labels of selected instances from a large pool of unlabeled data points. The objective is to produce a classifier of relatively low risk, as measured under the $0$-$1$ loss, ideally using fewer label requests than the number of random labeled data points sufficient to achieve the same. This work investigates the potential uses of surrogate loss functions in the context of active learning. Specifically, it presents an active learning algorithm based on an arbitrary classification-calibrated surrogate loss function, along with an analysis of the number of label requests sufficient for the classifier returned by the algorithm to achieve a given risk under the $0$-$1$ loss. Interestingly, these results cannot be obtained by simply optimizing the surrogate risk via active learning to an extent sufficient to provide a guarantee on the $0$-$1$ loss, as is common practice in the analysis of surrogate losses for passive learning. Some of the results have additional implications for the use of surrogate losses in passive learning.

Article information

Electron. J. Statist., Volume 13, Number 2 (2019), 4646-4708.

Received: June 2018
First available in Project Euclid: 13 November 2019

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Primary: 62L05: Sequential design 68Q32: Computational learning theory [See also 68T05] 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20] 68T05: Learning and adaptive systems [See also 68Q32, 91E40]
Secondary: 68T10: Pattern recognition, speech recognition {For cluster analysis, see 62H30} 68Q10: Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) [See also 68Q85] 68Q25: Analysis of algorithms and problem complexity [See also 68W40] 68W40: Analysis of algorithms [See also 68Q25] 62G99: None of the above, but in this section

Active learning sequential design selective sampling statistical learning theory surrogate loss functions classification

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Hanneke, Steve; Yang, Liu. Surrogate losses in passive and active learning. Electron. J. Statist. 13 (2019), no. 2, 4646--4708. doi:10.1214/19-EJS1635. https://projecteuclid.org/euclid.ejs/1573635664

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