  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.
