We propose a new neighbouring prediction model for mortality forecasting. For each mortality rate at age x in year t, mx,t, we construct an image of neighbourhood mortality data around mx,t, that is, Ꜫmx,t (x1, x2, s), which includes mortality information for ages in [x-x1, x+x2], lagging k years (1 ≤ k ≤ s). Combined with the deep learning model – convolutional neural network, this framework is able to capture the intricate nonlinear structure in the mortality data: the neighbourhood effect, which can go beyond the directions of period, age, and cohort as in classic mortality models. By performing an extensive empirical analysis on all the 41 countries and regions in the Human Mortality Database, we find that the proposed models achieve superior forecasting performance. This framework can be further enhanced to capture the patterns and interactions between multiple populations.

中文翻译：

---

死亡率的邻近预测

我们提出了一种用于死亡率预测的新邻近预测模型。对于每个年龄的死亡率X年吨,米x,t，我们构建了一个邻域死亡率数据的图像米x,t, 即 Ꜫ米x,t(X1,X2,s)，其中包括 [X-X1,X+X2]，滞后ķ年 (1 ≤ķ≤s）。结合深度学习模型——卷积神经网络，该框架能够捕捉死亡率数据中错综复杂的非线性结构：邻域效应，它可以超越经典死亡率模型中的时期、年龄和队列的方向。通过对人类死亡率数据库中的所有 41 个国家和地区进行广泛的实证分析，我们发现所提出的模型实现了优越的预测性能。可以进一步增强该框架以捕获多个群体之间的模式和相互作用。