Expressive Mortality Models through Gaussian Process Kernels
This work addresses the problem of modeling mortality data for demographers and actuaries, offering a flexible machine-learning approach that is incremental in its use of existing GP and genetic algorithm techniques.
The authors developed a Gaussian Process framework with a genetic programming algorithm to search for expressive kernels for modeling mortality surfaces, applying it to synthetic and real-world data from the Human Mortality Database to gain insights into cohort effects and smoothness across age and year dimensions.
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.