# Expressive Mortality Models through Gaussian Process Kernels

arXiv: https://arxiv.org/abs/2305.01728 · HTML: https://mlsanity.com/paper/2305.01728/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 49 references that are in the map.
- First posted on arXiv 2 May 2023.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Structure Discovery in Nonparametric Regression through Compositional Kernel Search](https://mlsanity.com/paper/1302.4922/) (2013)
- [Scalable Generalized Dynamic Topic Models](https://mlsanity.com/paper/1803.07868/) (2018)
- [Advanced Stationary and Non-Stationary Kernel Designs for Domain-Aware Gaussian Processes](https://mlsanity.com/paper/2102.03432/) (2021)
- [Gaussian Process Models for Mortality Rates and Improvement Factors](https://mlsanity.com/paper/1608.08291/) (2016)
- [Large-scale local surrogate modeling of stochastic simulation experiments](https://mlsanity.com/paper/2109.05324/) (2021)
- [Investigating the Parameter Space of Evolutionary Algorithms](https://mlsanity.com/paper/1706.04119/) (2017)

## Abstract (arXiv)

We develop a flexible Gaussian Process (GP) framework for learning the covariance structure of Age- and Year-specific mortality surfaces. Utilizing the additive and multiplicative structure of GP kernels, we design a genetic programming algorithm to search for the most expressive kernel for a given population. Our compositional search builds off the Age-Period-Cohort (APC) paradigm to construct a covariance prior best matching the spatio-temporal dynamics of a mortality dataset. We apply the resulting genetic algorithm (GA) on synthetic case studies to validate the ability of the GA to recover APC structure, and on real-life national-level datasets from the Human Mortality Database. Our machine-learning based analysis provides novel insight into the presence/absence of Cohort effects in different populations, and into the relative smoothness of mortality surfaces along the Age and Year dimensions. Our modelling work is done with the PyTorch libraries in Python and provides an in-depth investigation of employing GA to aid in compositional kernel search for GP surrogates.