Enhancing diagnostic of stochastic mortality models leveraging contrast trees: an application on Italian data

The rise in longevity in the twentieth century has led to a growing interest in modeling mortality, and new advanced techniques such as machine learning have recently joined to more traditional models, such as the Lee–Carter or the Age Period Cohort. However, the performances of these models, in terms of fitting to the observed data, are difficult to compare in a unified framework. The goodness-of-fit measures summarizing the discrepancy between the estimates from the model and the observed values are different for traditional mortality models and machine learning. We, therefore, employ a new technique, Contrast trees, which, leveraging on decision trees, provides a general approach for evaluating the quality of fit of different kinds of models by detecting the regions in the input space where models work poorly. Once the low-performance regions are detected, we use Contrast boosting to improve the inaccuracies of mortality estimates provided by each model. To verify the ability of this approach, we consider both standard stochastic mortality models and machine learning algorithms in the estimate of the Italian mortality rates from the Human Mortality Database. The results are discussed using both graphical and numerical tools, with particular attention to the high-error regions.