Smooth Min-Max Monotonic Networks

Christian Igel
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:20908-20923, 2024.

Abstract

Monotonicity constraints are powerful regularizers in statistical modelling. They can support fairness in computer-aided decision making and increase plausibility in data-driven scientific models. The seminal min-max (MM) neural network architecture ensures monotonicity, but often gets stuck in undesired local optima during training because of partial derivatives being zero when computing extrema. We propose a simple modification of the MM network using strictly-increasing smooth minimum and maximum functions that alleviates this problem. The resulting smooth min-max (SMM) network module inherits the asymptotic approximation properties from the MM architecture. It can be used within larger deep learning systems trained end-to-end. The SMM module is conceptually simple and computationally less demanding than state-of-the-art neural networks for monotonic modelling. Our experiments show that this does not come with a loss in generalization performance compared to alternative neural and non-neural approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-igel24a, title = {Smooth Min-Max Monotonic Networks}, author = {Igel, Christian}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {20908--20923}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/igel24a/igel24a.pdf}, url = {https://proceedings.mlr.press/v235/igel24a.html}, abstract = {Monotonicity constraints are powerful regularizers in statistical modelling. They can support fairness in computer-aided decision making and increase plausibility in data-driven scientific models. The seminal min-max (MM) neural network architecture ensures monotonicity, but often gets stuck in undesired local optima during training because of partial derivatives being zero when computing extrema. We propose a simple modification of the MM network using strictly-increasing smooth minimum and maximum functions that alleviates this problem. The resulting smooth min-max (SMM) network module inherits the asymptotic approximation properties from the MM architecture. It can be used within larger deep learning systems trained end-to-end. The SMM module is conceptually simple and computationally less demanding than state-of-the-art neural networks for monotonic modelling. Our experiments show that this does not come with a loss in generalization performance compared to alternative neural and non-neural approaches.} }
Endnote
%0 Conference Paper %T Smooth Min-Max Monotonic Networks %A Christian Igel %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-igel24a %I PMLR %P 20908--20923 %U https://proceedings.mlr.press/v235/igel24a.html %V 235 %X Monotonicity constraints are powerful regularizers in statistical modelling. They can support fairness in computer-aided decision making and increase plausibility in data-driven scientific models. The seminal min-max (MM) neural network architecture ensures monotonicity, but often gets stuck in undesired local optima during training because of partial derivatives being zero when computing extrema. We propose a simple modification of the MM network using strictly-increasing smooth minimum and maximum functions that alleviates this problem. The resulting smooth min-max (SMM) network module inherits the asymptotic approximation properties from the MM architecture. It can be used within larger deep learning systems trained end-to-end. The SMM module is conceptually simple and computationally less demanding than state-of-the-art neural networks for monotonic modelling. Our experiments show that this does not come with a loss in generalization performance compared to alternative neural and non-neural approaches.
APA
Igel, C.. (2024). Smooth Min-Max Monotonic Networks. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:20908-20923 Available from https://proceedings.mlr.press/v235/igel24a.html.

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