# Regularization-Based Methods for Ordinal Quantification

arXiv: https://arxiv.org/abs/2310.09210 · HTML: https://mlsanity.com/paper/2310.09210/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 58 references that are in the map.
- First posted on arXiv 13 Oct 2023.

## Builds on (most cited first, 7 of 7)

- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [SemEval-2017 Task 4: Sentiment Analysis in Twitter](https://mlsanity.com/paper/1912.00741/) (2019)
- [On the Consistency of Ordinal Regression Methods](https://mlsanity.com/paper/1408.2327/) (2014)
- [SemEval-2016 Task 4: Sentiment Analysis in Twitter](https://mlsanity.com/paper/1912.01973/) (2019)
- [A Recurrent Neural Network for Sentiment Quantification](https://mlsanity.com/paper/1809.00836/) (2018)
- [LeQua@CLEF2022: Learning to Quantify](https://mlsanity.com/paper/2111.11249/) (2021)

## Built on by (most cited first, 1 of 1)

- [Quantifying Feature Importance for Online Content Moderation](https://mlsanity.com/paper/2510.19882/) (2025)

## Abstract (arXiv)

Quantification, i.e., the task of training predictors of the class prevalence values in sets of unlabeled data items, has received increased attention in recent years. However, most quantification research has concentrated on developing algorithms for binary and multiclass problems in which the classes are not ordered. Here, we study the ordinal case, i.e., the case in which a total order is defined on the set of n>2 classes. We give three main contributions to this field. First, we create and make available two datasets for ordinal quantification (OQ) research that overcome the inadequacies of the previously available ones. Second, we experimentally compare the most important OQ algorithms proposed in the literature so far. To this end, we bring together algorithms proposed by authors from very different research fields, such as data mining and astrophysics, who were unaware of each others' developments. Third, we propose a novel class of regularized OQ algorithms, which outperforms existing algorithms in our experiments. The key to this gain in performance is that our regularization prevents ordinally implausible estimates, assuming that ordinal distributions tend to be smooth in practice. We informally verify this assumption for several real-world applications.