Optimal Threshold Labeling for Ordinal Regression Methods

Published: 18 Jan 2023, Last Modified: 28 Feb 2023Accepted by TMLREveryoneRevisionsBibTeX
Abstract: For an ordinal regression task, a classification task for ordinal data, one-dimensional transformation (1DT)-based methods are often employed since they are considered to capture the ordinal relation of ordinal data well. They learn a 1DT of the observation of the explanatory variables so that an observation with a larger class label tends to have a larger value of the 1DT, and classify the observation by labeling that learned 1DT. In this paper, we study the labeling procedure for 1DT-based methods, which have not been sufficiently discussed in existing studies. While regression-based methods and classical threshold methods conventionally use threshold labelings, which label a learned 1DT according to the rank of the interval to which the 1DT belongs among intervals on the real line separated by threshold parameters, we prove that likelihood-based labeling used in popular statistical 1DT-based methods is also a threshold labeling in typical usages. Moreover, we show that these threshold labelings can be sub-optimal ones depending on the learning result of the 1DT and the task under consideration. On the basis of these findings, we propose to apply empirical optimal threshold labeling, which is a threshold labeling that uses threshold parameters minimizing the empirical task risk for a learned 1DT, to those methods. In experiments with real-world datasets, changing the labeling procedure of existing 1DT-based methods to the proposed one improved the classification performance in many tried cases.
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Length: Long submission (more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=PInXz6Gasv&referrer=%5BAuthor%20Console%5D(%2Fgroup%3Fid%3DTMLR%2FAuthors%23your-submissions)
Changes Since Last Submission: I submit the camera-ready version.
Code: https://github.com/yamasakiryoya/OTL
Assigned Action Editor: ~Hsuan-Tien_Lin1
Submission Number: 600