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.

翻译：本文提出了深度功能因子模型（DF2M），这是一种用于分析高维功能时间序列的贝叶斯非参数模型。DF2M建立在印度自助餐过程和多任务高斯过程的基础上，并引入了一个能够捕捉非马尔可夫和非线性时间动态的深度核函数。与许多黑盒深度学习模型不同，DF2M通过构建因子模型并将深度神经网络集成到核函数中，提供了一种可解释的神经网络应用方法。此外，我们开发了一种计算高效的变分推断算法来推断DF2M。在四个真实世界数据集上的实证结果表明，对于高维功能时间序列，与传统的深度学习模型相比，DF2M提供了更好的可解释性和更优越的预测准确性。