# How to address monotonicity for model risk management?

arXiv: https://arxiv.org/abs/2305.00799 · HTML: https://mlsanity.com/paper/2305.00799/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 56 references that are in the map.
- First posted on arXiv 28 Apr 2023.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [An Intersectional Definition of Fairness](https://mlsanity.com/paper/1807.08362/) (2018)
- [Explaining Explanations: Axiomatic Feature Interactions for Deep Networks](https://mlsanity.com/paper/2002.04138/) (2020)
- [GAMI-Net: An Explainable Neural Network based on Generalized Additive Models with Structured Interactions](https://mlsanity.com/paper/2003.07132/) (2020)
- [An Empirical Study of Rich Subgroup Fairness for Machine Learning](https://mlsanity.com/paper/1808.08166/) (2018)
- [Detecting Statistical Interactions from Neural Network Weights](https://mlsanity.com/paper/1705.04977/) (2017)
- [How does this interaction affect me? Interpretable attribution for feature interactions](https://mlsanity.com/paper/2006.10965/) (2020)
- [Deep Lattice Networks and Partial Monotonic Functions](https://mlsanity.com/paper/1709.06680/) (2017)
- [Distill-and-Compare: Auditing Black-Box Models Using Transparent Model Distillation](https://mlsanity.com/paper/1710.06169/) (2017)
- [Certified Monotonic Neural Networks](https://mlsanity.com/paper/2011.10219/) (2020)
- [Monotonic Neural Additive Models: Pursuing Regulated Machine Learning Models for Credit Scoring](https://mlsanity.com/paper/2209.10070/) (2022)

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

- [RiskProp: Collision-Anchored Self-Supervised Risk Propagation for Early Accident Anticipation](https://mlsanity.com/paper/2603.27165/) (2026)
- [Attribution Methods in Asset Pricing: Do They Account for Risk?](https://mlsanity.com/paper/2407.08953/) (2024)
- [FinML-Chain: A Blockchain-Integrated Dataset for Enhanced Financial Machine Learning](https://mlsanity.com/paper/2411.16277/) (2024)
- [Explaining Risks: Axiomatic Risk Attributions for Financial Models](https://mlsanity.com/paper/2506.06653/) (2025)

## Abstract (arXiv)

In this paper, we study the problem of establishing the accountability and fairness of transparent machine learning models through monotonicity. Although there have been numerous studies on individual monotonicity, pairwise monotonicity is often overlooked in the existing literature. This paper studies transparent neural networks in the presence of three types of monotonicity: individual monotonicity, weak pairwise monotonicity, and strong pairwise monotonicity. As a means of achieving monotonicity while maintaining transparency, we propose the monotonic groves of neural additive models. As a result of empirical examples, we demonstrate that monotonicity is often violated in practice and that monotonic groves of neural additive models are transparent, accountable, and fair.