IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v114y2019i525p223-234.html
   My bibliography  Save this article

Least Ambiguous Set-Valued Classifiers With Bounded Error Levels

Author

Listed:
  • Mauricio Sadinle
  • Jing Lei
  • Larry Wasserman

Abstract

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.

Suggested Citation

  • Mauricio Sadinle & Jing Lei & Larry Wasserman, 2019. "Least Ambiguous Set-Valued Classifiers With Bounded Error Levels," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 223-234, January.
  • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:525:p:223-234
    DOI: 10.1080/01621459.2017.1395341
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2017.1395341
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/01621459.2017.1395341?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lihua Lei & Emmanuel J. Candès, 2021. "Conformal inference of counterfactuals and individual treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 911-938, November.
    2. Leying Guan & Robert Tibshirani, 2022. "Prediction and outlier detection in classification problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 524-546, April.
    3. Wei Liu & Frank Bretz & Natchalee Srimaneekarn & Jianan Peng & Anthony J. Hayter, 2019. "Confidence Sets for Statistical Classification," Stats, MDPI, vol. 2(3), pages 1-15, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:114:y:2019:i:525:p:223-234. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.