Mortality Forecasting as a Flow Field in Tucker Decomposition Space

TL;DR

This paper introduces a novel mortality forecasting method using a flow field in Tucker decomposition space, significantly reducing bias and error compared to traditional models across extensive cross-validation tests.

Contribution

It reframes mortality forecasting as a flow in low-dimensional space, improving accuracy and bias over existing models by leveraging Tucker tensor decomposition and PCA.

Findings

Flow-field method reduces bias to +1.058 years, outperforming Lee-Carter and others.

Achieves 2.7x lower error than UN model on large test set.

Provides accurate age-specific mortality schedules at long horizons.

Abstract

Mortality forecasting methods in the Lee-Carter tradition extrapolate temporal components via time-series models, often producing forecasts that systematically underpredict life expectancy at long horizons. This bias is consequential for planning pension funding, healthcare capacity, and social security solvency. The dominant alternative - the Bayesian double-logistic model underlying the UN World Population Prospects - forecasts scalar life expectancy and requires a separate model life table system to recover age-specific rates. We reframe forecasting as integrating a flow field through the low-dimensional score space of a Tucker tensor decomposition of the Human Mortality Database. PCA reduction reveals that the mortality transition is essentially a one-dimensional flow: a scalar speed function advances the level, trajectory functions supply the structural scores, and the Tucker reconstruction produces complete sex-specific, single-year-of-age mortality schedules at each horizon. In leave-country-out cross-validation (9,507 test points, 50-year horizon), the flow-field achieves bias of +1.058 years - substantially smaller than Lee-Carter (-3.2), Hyndman-Ullah (-3.5), and pyBayesLife (+3.3) - because it navigates a score space parameterised by mortality level rather than extrapolating temporal trends into unobserved territory. On 1.66 million sex-age-specific test points, it achieves 2.7x lower error than our de novo Python reimplementation of the UN pipeline trained on the same data - with lower error at every age, every forecast horizon, and for both sexes.