Classification with Noisy Labels by Importance Reweighting

In this paper, we study a classification problem in which sample labels are randomly corrupted. In this scenario, there is an unobservable sample with noise-free labels. However, before being observed, the true labels are independently flipped with a probability <inline-formula><tex-math>...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence Vol. 38; no. 3; pp. 447 - 461
Main Authors: Liu, Tongliang, Tao, Dacheng
Format: Journal Article
Language:English
Published: United States IEEE 01.03.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Classification
consistency
Convergence
Estimation
importance reweighting
Kernel
label noise
Noise
Noise measurement
noise rate estimation
Robustness
label noise
noise rate estimation
importance reweighting
consistency
Classification
ISSN:0162-8828, 1939-3539, 2160-9292, 1939-3539
Online Access:Get full text
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Summary:In this paper, we study a classification problem in which sample labels are randomly corrupted. In this scenario, there is an unobservable sample with noise-free labels. However, before being observed, the true labels are independently flipped with a probability <inline-formula><tex-math>\rho \in [0,0.5)</tex-math> <inline-graphic xlink:type="simple" xlink:href="tao-ieq1-2456899.gif"/> </inline-formula>, and the random label noise can be class-conditional. Here, we address two fundamental problems raised by this scenario. The first is how to best use the abundant surrogate loss functions designed for the traditional classification problem when there is label noise. We prove that any surrogate loss function can be used for classification with noisy labels by using importance reweighting, with consistency assurance that the label noise does not ultimately hinder the search for the optimal classifier of the noise-free sample. The other is the open problem of how to obtain the noise rate <inline-formula> <tex-math>\rho</tex-math> <inline-graphic xlink:type="simple" xlink:href="tao-ieq2-2456899.gif"/> </inline-formula>. We show that the rate is upper bounded by the conditional probability <inline-formula><tex-math> P(\hat{Y}|X)</tex-math> <inline-graphic xlink:type="simple" xlink:href="tao-ieq3-2456899.gif"/> </inline-formula> of the noisy sample. Consequently, the rate can be estimated, because the upper bound can be easily reached in classification problems. Experimental results on synthetic and real datasets confirm the efficiency of our methods.
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ISSN:0162-8828
1939-3539
2160-9292
1939-3539
DOI:10.1109/TPAMI.2015.2456899