Least Ambiguous Set-Valued Classifiers With Bounded Error Levels

In most classification tasks, there are observations that are ambiguous and therefore difficult to correctly label. Set-valued classifiers output sets of plausible labels rather than a single label, thereby giving a more appropriate and informative treatment to the labeling of ambiguous instances. W...

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Veröffentlicht in:Journal of the American Statistical Association Jg. 114; H. 525; S. 223 - 234
Hauptverfasser: Sadinle, Mauricio, Lei, Jing, Wasserman, Larry
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Alexandria Taylor & Francis 02.01.2019
Taylor & Francis Group,LLC
Taylor & Francis Ltd
Schlagworte:
Ambiguity
Ambiguous observation
Asymptotic properties
Bayes classifier
Classification
Classifiers
Conditional probability
equations
Estimators
Labeling
Labels
Multiclass classification
Nondeterministic classifier
Oracle classifier
Probability
Property
Regression analysis
Reject option
Statistical methods
Statistics
Theory and Methods
ISSN:0162-1459, 1537-274X, 1537-274X
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Zusammenfassung:In most classification tasks, there are observations that are ambiguous and therefore difficult to correctly label. Set-valued classifiers output sets of plausible labels rather than a single label, thereby giving a more appropriate and informative treatment to the labeling of ambiguous instances. We introduce a framework for multiclass set-valued classification, where the classifiers guarantee user-defined levels of coverage or confidence (the probability that the true label is contained in the set) while minimizing the ambiguity (the expected size of the output). We first derive oracle classifiers assuming the true distribution to be known. We show that the oracle classifiers are obtained from level sets of the functions that define the conditional probability of each class. Then we develop estimators with good asymptotic and finite sample properties. The proposed estimators build on existing single-label classifiers. The optimal classifier can sometimes output the empty set, but we provide two solutions to fix this issue that are suitable for various practical needs. Supplementary materials for this article are available online.
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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2017.1395341