# Monotonic Neural Additive Models: Pursuing Regulated Machine Learning Models for Credit Scoring

arXiv: https://arxiv.org/abs/2209.10070 · HTML: https://mlsanity.com/paper/2209.10070/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 21 Sep 2022.

## Builds on (most cited first, 13 of 13)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [GAMI-Net: An Explainable Neural Network based on Generalized Additive Models with Structured Interactions](https://mlsanity.com/paper/2003.07132/) (2020)
- [Deep Lattice Networks and Partial Monotonic Functions](https://mlsanity.com/paper/1709.06680/) (2017)
- [Certified Monotonic Neural Networks](https://mlsanity.com/paper/2011.10219/) (2020)
- [An Interpretable Model with Globally Consistent Explanations for Credit Risk](https://mlsanity.com/paper/1811.12615/) (2018)
- [Enhancing Explainability of Neural Networks through Architecture Constraints](https://mlsanity.com/paper/1901.03838/) (2019)
- [Designing Inherently Interpretable Machine Learning Models](https://mlsanity.com/paper/2111.01743/) (2021)
- [Significance Tests for Neural Networks](https://mlsanity.com/paper/1902.06021/) (2019)
- [Sensitivity based Neural Networks Explanations](https://mlsanity.com/paper/1812.01029/) (2018)
- [Multicriteria interpretability driven Deep Learning](https://mlsanity.com/paper/2111.14088/) (2021)
- [Seven challenges for harmonizing explainability requirements](https://mlsanity.com/paper/2108.05390/) (2021)

## Built on by (most cited first, 12 of 12)

- [A Comprehensive Review on Financial Explainable AI](https://mlsanity.com/paper/2309.11960/) (2023)
- [Monotonicity for AI ethics and society: An empirical study of the monotonic neural additive model in criminology, education, health care, and finance](https://mlsanity.com/paper/2301.07060/) (2023)
- [How to address monotonicity for model risk management?](https://mlsanity.com/paper/2305.00799/) (2023)
- [Tensor Product Neural Networks for Functional ANOVA Model](https://mlsanity.com/paper/2502.15215/) (2025)
- [Explainable Automatic Grading with Neural Additive Models](https://mlsanity.com/paper/2405.00489/) (2024)
- [Can I Trust the Explanations? Investigating Explainable Machine Learning Methods for Monotonic Models](https://mlsanity.com/paper/2309.13246/) (2023)
- [Neural Additive Image Model: Interpretation through Interpolation](https://mlsanity.com/paper/2405.02295/) (2024)
- [Explaining Risks: Axiomatic Risk Attributions for Financial Models](https://mlsanity.com/paper/2506.06653/) (2025)
- [An Interpretable Deep Learning Model for General Insurance Pricing](https://mlsanity.com/paper/2509.08467/) (2025)
- [TRUST-SCF: Transformer-based Risk Understanding and Scoring for Transactional Supply Chain Finance](https://mlsanity.com/paper/2606.08140/) (2026)
- [Implementing neural network mixed-effects models in Template Model Builder (TMB)](https://mlsanity.com/paper/2608.31133/) (2026)
- [Interpretable and Fair Generalized Additive Neural Networks via Multi-objective Learning](https://mlsanity.com/paper/2609.05946/) (2026)

## Abstract (arXiv)

The forecasting of credit default risk has been an active research field for several decades. Historically, logistic regression has been used as a major tool due to its compliance with regulatory requirements: transparency, explainability, and fairness. In recent years, researchers have increasingly used complex and advanced machine learning methods to improve prediction accuracy. Even though a machine learning method could potentially improve the model accuracy, it complicates simple logistic regression, deteriorates explainability, and often violates fairness. In the absence of compliance with regulatory requirements, even highly accurate machine learning methods are unlikely to be accepted by companies for credit scoring. In this paper, we introduce a novel class of monotonic neural additive models, which meet regulatory requirements by simplifying neural network architecture and enforcing monotonicity. By utilizing the special architectural features of the neural additive model, the monotonic neural additive model penalizes monotonicity violations effectively. Consequently, the computational cost of training a monotonic neural additive model is similar to that of training a neural additive model, as a free lunch. We demonstrate through empirical results that our new model is as accurate as black-box fully-connected neural networks, providing a highly accurate and regulated machine learning method.