  This paper introduces the Deep Functional Factor Model (DF2M), a Bayesian
nonparametric model designed for analysis of high-dimensional functional time
series. DF2M is built upon the Indian Buffet Process and the multi-task
Gaussian Process, incorporating a deep kernel function that captures
non-Markovian and nonlinear temporal dynamics. Unlike many black-box deep
learning models, DF2M offers an explainable approach to utilizing neural
networks by constructing a factor model and integrating deep neural networks
within the kernel function. Additionally, we develop a computationally
efficient variational inference algorithm to infer DF2M. Empirical results from
four real-world datasets demonstrate that DF2M provides better explainability
and superior predictive accuracy compared to conventional deep learning models
for high-dimensional functional time series.
