In this paper, we present Deep Functional Factor Model (DF2M), a Bayesian nonparametric model for analyzing high-dimensional functional time series. The DF2M makes use of the Indian Buffet Process and the multi-task Gaussian Process with a deep kernel function to capture non-Markovian and nonlinear temporal dynamics. Unlike many black-box deep learning models, the DF2M provides an explainable way to use neural networks by constructing a factor model and incorporating deep neural networks within the kernel function. Additionally, we develop a computationally efficient variational inference algorithm for inferring the DF2M. Empirical results from four real-world datasets demonstrate that the DF2M offers better explainability and superior predictive accuracy compared to conventional deep learning models for high-dimensional functional time series.

翻译：本文提出深度函数因子模型（DF2M），这是一种用于分析高维函数型时间序列的贝叶斯非参数模型。DF2M利用印度自助餐过程与具有深度核函数的多任务高斯过程，捕捉非马尔可夫与非线性的时间动态特性。与许多黑箱深度学习模型不同，DF2M通过构建因子模型并在核函数中嵌入深度神经网络，提供了一种利用神经网络的可解释方式。此外，我们开发了一种计算高效的变分推断算法来对DF2M进行推断。基于四个真实数据集的实证结果表明，在高维函数型时间序列分析中，DF2M相较于传统深度学习模型具有更优的可解释性与预测精度。