# Smoothness and monotonicity constraints for neural networks using ICEnet

**Authors:** Ronald Richman, Mario Wüthrich  
**arXiv:** [2305.08807](https://arxiv.org/abs/2305.08807)  
**Date:** 2023-05-15  
**Summary page:** https://www.summarizepaper.com/en/paper/2305.08807v1/

## Key points

- Deep neural networks are increasingly popular in actuarial tasks due to their superior accuracy compared to traditional methods.
- Generalized Linear Models (GLMs) used in the industry can easily incorporate smoothness and monotonicity constraints for insurance risk factors.
- There is currently no established method for implementing these constraints in deep neural networks, which poses a significant barrier to their adoption in insurance practice.
- Ronald Richman and Mario Wüthrich proposed a novel method called ICEnet that allows for the incorporation of smoothness and monotonicity constraints within deep neural network models.
- The authors demonstrate how ICEnet can be trained using real-world datasets and provide example applications to showcase its effectiveness.
- The proposed method is named ICEnet to highlight its close connection with the individual conditional expectation (ICE) model interpretability technique.
- With the ability to enforce smoothness and monotonicity constraints within deep neural networks, ICEnet offers an important tool for actuaries seeking to improve accuracy while maintaining necessary constraints in their models.

## Summary

The use of deep neural networks has become increasingly popular in actuarial tasks due to their superior accuracy compared to traditional methods. Generalized Linear Models (GLMs) used in the industry can easily incorporate smoothness and monotonicity constraints for insurance risk factors, however there is currently no established method for implementing these constraints in deep neural networks. This lack of constraint enforcement poses a significant barrier to the adoption of neural networks in insurance practice. To address this issue, Ronald Richman and Mario Wüthrich proposed a novel method called ICEnet that allows for the incorporation of smoothness and monotonicity constraints within deep neural network models. The authors demonstrate how ICEnet can be trained using real-world datasets and provide example applications to showcase its effectiveness. The proposed method is named ICEnet to highlight its close connection with the individual conditional expectation (ICE) model interpretability technique. With the ability to enforce smoothness and monotonicity constraints within deep neural networks, ICEnet offers an important tool for actuaries seeking to improve accuracy while maintaining necessary constraints in their models.