ABSTRACT In this paper, we formulate the multi-population mortality forecasting problem based on 3-way (age, year, and country/gender) decompositions. By applying the canonical polyadic decomposition (CPD) and the different forms of the Tucker decomposition to multi-population mortality data (10 European countries and 2 genders), we find that the out-of-sample forecasting performance is significantly improved both for individual populations and the aggregate population compared with using the single-population mortality model based on rank-1 singular value decomposition (SVD), or the Lee–Carter model. The results also shed lights on the similarity and difference of mortality among different countries. Additionally, we compare the variance-explained method and the out-of-sample validation method for rank (hyper-parameter) selection. Results show that the out-of-sample validation method is preferred for forecasting purposes.

中文翻译：

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使用张量分解进行多人口死亡率预测

摘要在本文中，我们制定了基于 3 向（年龄、年份和国家/性别）分解的多人口死亡率预测问题。通过将典型多元分解 (CPD) 和不同形式的 Tucker 分解应用于多人口死亡率数据（10 个欧洲国家和 2 个性别），我们发现样本外预测性能对于个体人口都有显着提高总人口与使用基于 1 阶奇异值分解 (SVD) 的单一人口死亡率模型或 Lee-Carter 模型进行比较。结果还阐明了不同国家死亡率的相似性和差异性。此外，我们比较了方差解释方法和用于秩（超参数）选择的样本外验证方法。