# Parallel Algorithm for Optimal Threshold Labeling of Ordinal Regression Methods

arXiv: https://arxiv.org/abs/2405.12756 · HTML: https://mlsanity.com/paper/2405.12756/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 21 references that are in the map.
- First posted on arXiv 21 May 2024.

## Builds on (most cited first, 3 of 3)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Rank consistent ordinal regression for neural networks with application to age estimation](https://mlsanity.com/paper/1901.07884/) (2019)
- [On the Consistency of Ordinal Regression Methods](https://mlsanity.com/paper/1408.2327/) (2014)

## Built on by (most cited first, 4 of 4)

- [Remarks on Loss Function of Threshold Method for Ordinal Regression Problem](https://mlsanity.com/paper/2405.13288/) (2024)
- [Approximately Unimodal Likelihood Models for Ordinal Regression](https://mlsanity.com/paper/2510.00122/) (2025)
- [Voice Biomarkers for Depression and Anxiety](https://mlsanity.com/paper/2605.09908/) (2026)
- [Unimodality-Promoting Regularized Learning for Ordinal Regression](https://mlsanity.com/paper/2608.08359/) (2026)

## Abstract (arXiv)

Ordinal regression (OR) is classification of ordinal data in which the underlying categorical target variable has a natural ordinal relation for the underlying explanatory variable. For K-class OR tasks, threshold methods learn a one-dimensional transformation (1DT) of the explanatory variable so that 1DT values for observations of the explanatory variable preserve the order of label values 1,ldots,K for corresponding observations of the target variable well, and then assign a label prediction to the learned 1DT through threshold labeling, namely, according to the rank of an interval to which the 1DT belongs among intervals on the real line separated by (K-1) threshold parameters. In this study, we propose a parallelizable algorithm to find the optimal threshold labeling, which was developed in previous research, and derive sufficient conditions for that algorithm to successfully output the optimal threshold labeling. In a numerical experiment we performed, the computation time taken for the whole learning process of a threshold method with the optimal threshold labeling could be reduced to approximately 60,% by using the proposed algorithm with parallel processing compared to using an existing algorithm based on dynamic programming.