# Monotonic classification: an overview on algorithms, performance measures and data sets

arXiv: https://arxiv.org/abs/1811.07155 · HTML: https://mlsanity.com/paper/1811.07155/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2018.

## Built on by (most cited first, 18 of 18)

- [Explanations for Monotonic Classifiers](https://mlsanity.com/paper/2106.00154/) (2021)
- [Improving Screening Processes via Calibrated Subset Selection](https://mlsanity.com/paper/2202.01147/) (2022)
- [Cardinality-Minimal Explanations for Monotonic Neural Networks](https://mlsanity.com/paper/2205.09901/) (2022)
- [Aligning Model Properties via Conformal Risk Control](https://mlsanity.com/paper/2406.18777/) (2024)
- [Smooth Min-Max Monotonic Networks](https://mlsanity.com/paper/2306.01147/) (2023)
- [Explaining Adverse Actions in Credit Decisions Using Shapley Decomposition](https://mlsanity.com/paper/2204.12365/) (2022)
- [Constrained Classification and Policy Learning](https://mlsanity.com/paper/2106.12886/) (2021)
- [A Novel Machine Learning Approach to Data Inconsistency with respect to a Fuzzy Relation](https://mlsanity.com/paper/2111.13447/) (2021)
- [A mathematical certification for positivity conditions in Neural Networks with applications to partial monotonicity and Trustworthy AI](https://mlsanity.com/paper/2406.08525/) (2024)
- [On Aligning Prediction Models with Clinical Experiential Learning: A Prostate Cancer Case Study](https://mlsanity.com/paper/2509.04053/) (2025)
- [Monotonic Kolmogorov-Arnold Networks: A Theoretical and Empirical Study of Monotonicity as an Inductive Bias](https://mlsanity.com/paper/2606.17886/) (2026)
- [Learning MR-Sort Models from Non-Monotone Data](https://mlsanity.com/paper/2107.09668/) (2021)
- [Semi-supervised Clustering with Two Types of Background Knowledge: Fusing Pairwise Constraints and Monotonicity Constraints](https://mlsanity.com/paper/2302.14060/) (2023)
- [Tackling water table depth modeling via machine learning: From proxy observations to verifiability](https://mlsanity.com/paper/2405.04579/) (2024)
- [Monotonic anomaly detection](https://mlsanity.com/paper/2410.23158/) (2024)
- [A Novel Multi-Objective Evolutionary Algorithm for Counterfactual Generation](https://mlsanity.com/paper/2502.10418/) (2025)
- [Computing frustration and near-monotonicity in deep neural networks](https://mlsanity.com/paper/2510.05286/) (2025)
- [The Cost of a Physics Prior Is Bounded by the Ablation Gap](https://mlsanity.com/paper/2608.21059/) (2026)

## Abstract (arXiv)

Currently, knowledge discovery in databases is an essential step to identify valid, novel and useful patterns for decision making. There are many real-world scenarios, such as bankruptcy prediction, option pricing or medical diagnosis, where the classification models to be learned need to fulfil restrictions of monotonicity (i.e. the target class label should not decrease when input attributes values increase). For instance, it is rational to assume that a higher debt ratio of a company should never result in a lower level of bankruptcy risk. Consequently, there is a growing interest from the data mining research community concerning monotonic predictive models. This paper aims to present an overview about the literature in the field, analyzing existing techniques and proposing a taxonomy of the algorithms based on the type of model generated. For each method, we review the quality metrics considered in the evaluation and the different data sets and monotonic problems used in the analysis. In this way, this paper serves as an overview of the research about monotonic classification in specialized literature and can be used as a functional guide of the field.