Neural networks for simultaneous modeling of multi-population mortality with coherent forecasts

We use deep learning models for modeling mortality data for multiple populations simultaneously, sharing information across populations to obtain a common factor, while allowing for short-term deviations for individual populations. We propose a unified multi-task deep learning structure based on the Augmented Common Factor (ACF) model [Li, N., & Lee, R. (2005). Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography, 42, 575–594. https://doi.org/10.1353/dem.2005.0021], which enforces coherence in mortality forecasts, a desirable property where the long-term ratio of mortality rates between populations does not diverge but rather maintains a fixed value. With DeepACF we use fully-connected layers in both the shared and private branches of the architecture, with a three-component loss function to reduce the prediction errors of these two branches while ensuring their orthogonality. In order to better capture temporal correlation in mortality data, we introduce ConvACF and TransACF where we replace the first fully-connected layer in DeepACF with a convolutional neural network (CNN) and transformer respectively. Results from an empirical study applying these models to three datasets of mortality rates in multiple countries show the effectiveness of our models for performing mortality forecasts.