Modified Threshold Method for Ordinal Regression
Abstract: Ordinal regression (OR, also called ordinal classification) is the classification of ordinal data in which the underlying target variable is discrete and has a natural ordinal relation. For OR problems, threshold methods are often employed since they are considered to capture the ordinal relation of data well: they learn a one-dimensional transformation (1DT) of an observation of the explanatory variables and classify the data by labeling that learned 1DT according to the rank of the interval to which the 1DT belongs among intervals on the real line separated by threshold parameters. In many conventional methods, the threshold parameters are determined regardless of the learning result of the 1DT and the task under consideration. Such conventional settings may deteriorate the classification performance. We, therefore, propose a novel computationally efficient method for determining the threshold parameters: it learns each threshold parameter independently through solving a problem relaxed from the minimization of the empirical task risk for the learned 1DT. The proposed labeling procedure experimentally gave superior classification performance with a feasible degree of additional computational load compared to four related existing labeling procedures in many of tried cases.
Submission Length: Long submission (more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=c1juOUE7Yx&referrer=%5BTMLR%5D(%2Fgroup%3Fid%3DTMLR)
Changes Since Last Submission: Dear all reviewers
We greatly appreciate your constructive reviews.
We submitted a revised version.
To save each reviewer the labor of looking at the other reviewers' comments and our responses, we summarize here our statements and changes of particular importance.
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We add Section 4.4, "Relationship to Previous Works", as reply to Action Editors' comments.
The discussion of this study remains the same after this change, but it further clarifies relation to previous studies.
Note that, during the writing of the first draft, these previous works were omitted from the paper because they are currently minor (other works do not adopt their idea).
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We largely modified Section 5, as reply to comments by reviewers YTfd and jaFP.
We performed additional experiments for various-domain datasets.
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We add the second paragraph in Section 6, as reply to comments by reviewer K5i6.
This relates to the two-step optimization consisting of the surrogate risk minimization and threshold parameters optimization.
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In the revised version, we emphasize terminologies by "\textit{\textbf{~}}" (if this violates the style of TMLR, let us know it).
Assigned Action Editor: ~Hsuan-Tien_Lin1
Submission Number: 274
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