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Smoothness and monotonicity constraints for neural networks using ICEnet

Published online by Cambridge University Press:  01 April 2024

Ronald Richman Open the ORCID record for Ronald Richman [Opens in a new window]  and
Mario V. Wüthrich
Ronald Richman*
Affiliation:
University of the Witwatersrand, Johannesburg, South Africa Old Mutual Insure, Johannesburg, South Africa
Mario V. Wüthrich
Affiliation:
RiskLab, Department of Mathematics, ETH Zurich, Zürich, Switzerland
*
Corresponding author: Ronald Richman; Email: ronaldrichman@gmail.com
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Abstract

Deep neural networks have become an important tool for use in actuarial tasks, due to the significant gains in accuracy provided by these techniques compared to traditional methods, but also due to the close connection of these models to the generalized linear models (GLMs) currently used in industry. Although constraining GLM parameters relating to insurance risk factors to be smooth or exhibit monotonicity is trivial, methods to incorporate such constraints into deep neural networks have not yet been developed. This is a barrier for the adoption of neural networks in insurance practice since actuaries often impose these constraints for commercial or statistical reasons. In this work, we present a novel method for enforcing constraints within deep neural network models, and we show how these models can be trained. Moreover, we provide example applications using real-world datasets. We call our proposed method ICEnet to emphasize the close link of our proposal to the individual conditional expectation model interpretability technique.

Keywords

SmoothingWhittaker–Henderson smoothinggraduationmonotonicitydeep neural networksconstrained likelihoodindividual conditional expectation
Type
Original Research Paper
Information
Annals of Actuarial Science , First View , pp. 1 - 28
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

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