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Title: Classification with asymmetric label noise: Consistency and maximal denoising

Abstract

In many real-world classification problems, the labels of training examples are randomly corrupted. Most previous theoretical work on classification with label noise assumes that the two classes are separable, that the label noise is independent of the true class label, or that the noise proportions for each class are known. In this work, we give conditions that are necessary and sufficient for the true class-conditional distributions to be identifiable. These conditions are weaker than those analyzed previously, and allow for the classes to be nonseparable and the noise levels to be asymmetric and unknown. The conditions essentially state that a majority of the observed labels are correct and that the true class-conditional distributions are “mutually irreducible,” a concept we introduce that limits the similarity of the two distributions. For any label noise problem, there is a unique pair of true class-conditional distributions satisfying the proposed conditions, and we argue that this pair corresponds in a certain sense to maximal denoising of the observed distributions. Our results are facilitated by a connection to “mixture proportion estimation,” which is the problem of estimating the maximal proportion of one distribution that is present in another. We establish a novel rate of convergence resultmore » for mixture proportion estimation, and apply this to obtain consistency of a discrimination rule based on surrogate loss minimization. Experimental results on benchmark data and a nuclear particle classification problem demonstrate the efficacy of our approach. MSC 2010 subject classifications: Primary 62H30; secondary 68T10. Keywords and phrases: Classification, label noise, mixture proportion estimation, surrogate loss, consistency.« less

Authors:
 [1];  [2];  [3];  [4];  [5]
  1. Univ. of Potsdam (Germany). Inst. for Mathematics
  2. Pennsylvania State Univ., University Park, PA (United States). Dept. of Mechanical and Nuclear Engineering
  3. Univ. of Utah, Salt Lake City, UT (United States). Dept. of Mathematics
  4. Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Nuclear Engineering and Radiological Sciences
  5. Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Electrical and Computer Engineering, Statistics
Publication Date:
Research Org.:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA), Office of Nonproliferation and Verification Research and Development (NA-22)
OSTI Identifier:
1366694
Grant/Contract Number:  
NA0002534
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Electronic Journal of Statistics
Additional Journal Information:
Journal Volume: 10; Journal Issue: 2; Journal ID: ISSN 1935-7524
Publisher:
Institute of Mathematical Statistics (IMS) and the Bernoulli Society
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Classification, label noise, mixture proportion estimation, surrogate loss, consistency

Citation Formats

Blanchard, Gilles, Flaska, Marek, Handy, Gregory, Pozzi, Sara, and Scott, Clayton. Classification with asymmetric label noise: Consistency and maximal denoising. United States: N. p., 2016. Web. doi:10.1214/16-EJS1193.
Blanchard, Gilles, Flaska, Marek, Handy, Gregory, Pozzi, Sara, & Scott, Clayton. Classification with asymmetric label noise: Consistency and maximal denoising. United States. https://doi.org/10.1214/16-EJS1193
Blanchard, Gilles, Flaska, Marek, Handy, Gregory, Pozzi, Sara, and Scott, Clayton. 2016. "Classification with asymmetric label noise: Consistency and maximal denoising". United States. https://doi.org/10.1214/16-EJS1193. https://www.osti.gov/servlets/purl/1366694.
@article{osti_1366694,
title = {Classification with asymmetric label noise: Consistency and maximal denoising},
author = {Blanchard, Gilles and Flaska, Marek and Handy, Gregory and Pozzi, Sara and Scott, Clayton},
abstractNote = {In many real-world classification problems, the labels of training examples are randomly corrupted. Most previous theoretical work on classification with label noise assumes that the two classes are separable, that the label noise is independent of the true class label, or that the noise proportions for each class are known. In this work, we give conditions that are necessary and sufficient for the true class-conditional distributions to be identifiable. These conditions are weaker than those analyzed previously, and allow for the classes to be nonseparable and the noise levels to be asymmetric and unknown. The conditions essentially state that a majority of the observed labels are correct and that the true class-conditional distributions are “mutually irreducible,” a concept we introduce that limits the similarity of the two distributions. For any label noise problem, there is a unique pair of true class-conditional distributions satisfying the proposed conditions, and we argue that this pair corresponds in a certain sense to maximal denoising of the observed distributions. Our results are facilitated by a connection to “mixture proportion estimation,” which is the problem of estimating the maximal proportion of one distribution that is present in another. We establish a novel rate of convergence result for mixture proportion estimation, and apply this to obtain consistency of a discrimination rule based on surrogate loss minimization. Experimental results on benchmark data and a nuclear particle classification problem demonstrate the efficacy of our approach. MSC 2010 subject classifications: Primary 62H30; secondary 68T10. Keywords and phrases: Classification, label noise, mixture proportion estimation, surrogate loss, consistency.},
doi = {10.1214/16-EJS1193},
url = {https://www.osti.gov/biblio/1366694}, journal = {Electronic Journal of Statistics},
issn = {1935-7524},
number = 2,
volume = 10,
place = {United States},
year = {Tue Sep 20 00:00:00 EDT 2016},
month = {Tue Sep 20 00:00:00 EDT 2016}
}

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