用概率神经网络同时捕捉高维时序数据的复杂趋势与不确定性。
Probabilistic Functional Neural Networks
- 结合前馈网络与概率建模，通过蒙特卡洛采样生成预测分布。
- 在日本死亡率数据上表现优于传统方法，提升预测精度并量化误差。
- 适合需要可信不确定性的高维时序预测场景，如公共卫生与金融。
高维函数型时间序列（HDFTS）常表现出非线性趋势和高空间维度，其建模与预测因非线性、非平稳性和高维度而面临独特挑战。本文提出一种新型概率函数神经网络（ProFnet），融合前馈神经网络与深度学习的优势，结合概率建模实现不确定性量化。该模型利用蒙特卡洛采样生成概率化预测，同时捕获多个区域间的时空依赖关系。在处理日本死亡率数据时，展现出卓越性能，显著提升预测准确率并提供可解释的置信区间。ProFnet为大规模高维函数型数据提供了可扩展且统一的解决方案，是复杂时序数据预测的重要工具。
原文摘要 · Abstract (English)
High-dimensional functional time series (HDFTS) are often characterized by nonlinear trends and high spatial dimensions. Such data poses unique challenges for modeling and forecasting due to the nonlinearity, nonstationarity, and high dimensionality. We propose a novel probabilistic functional neural network (ProFnet) to address these challenges. ProFnet integrates the strengths of feedforward and deep neural networks with probabilistic modeling. The model generates probabilistic forecasts using Monte Carlo sampling and also enables the quantification of uncertainty in predictions. While capturing both temporal and spatial dependencies across multiple regions, ProFnet offers a scalable and unified solution for large datasets. Applications to Japan's mortality rates demonstrate superior performance. This approach enhances predictive accuracy and provides interpretable uncertainty estimates, making it a valuable tool for forecasting complex high-dimensional functional data and HDFTS.
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