Probabilistic Functional Neural Networks
This provides a scalable and unified solution for forecasting complex high-dimensional functional data, though it appears incremental as it integrates existing neural network and probabilistic modeling approaches.
The paper tackled forecasting high-dimensional functional time series with nonlinear trends and high spatial dimensions by proposing a probabilistic functional neural network (ProFnet), which demonstrated superior performance in applications to Japan's mortality rates.
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.