Deep Latent Factor Model for Spatio-Temporal Forecasting

Latent factor models can perform spatio-temporal forecasting (i.e., predicting future responses at unmeasured as well as measured locations) by modeling temporal dependence using latent factors and considering spatial dependence using a spatial prior on factor loadings. However, they may fail to capture complex spatio-temporal dependence because the latent factors are typically assumed to follow a classical linear time series model, such as a vector autoregressive model. In this article, we propose a deep latent factor model for spatio-temporal forecasting that can model complex spatio-temporal dependence more flexibly by leveraging the high expressive power of a deep neural network. Specifically, the latent factors are modeled using a recurrent neural network and the factor loadings are modeled using a distance-based Gaussian process. The proposed model allows the number of latent factors to be inferred from the data using a beta-Bernoulli process, which enables computationally more efficient implementation compared to previous methods. We derive a stochastic variational inference algorithm for scalable inference of the proposed model and validate the model using simulated and real data examples.

隐因子模型（latent factor models）可实现时空预测（spatio-temporal forecasting）任务，即对未观测与已观测位置处的未来响应进行预测，其核心思路为利用隐因子建模时间依赖关系，并通过因子载荷上的空间先验考量空间依赖。然而，这类模型往往难以捕捉复杂的时空依赖关系，因为通常假设隐因子服从经典线性时间序列模型，例如向量自回归模型（vector autoregressive model）。本文针对时空预测任务提出一种深度隐因子模型，借助深度神经网络的高表达能力，能够更灵活地建模复杂时空依赖关系。具体而言，该模型采用循环神经网络（recurrent neural network）对隐因子进行建模，并通过基于距离的高斯过程（distance-based Gaussian process）对因子载荷进行建模。所提模型支持通过beta-伯努利过程（beta-Bernoulli process）从数据中推断隐因子的数量，相较于此前的方法，该设计可实现计算效率更优的模型实现。本文推导了适用于该模型的可扩展随机变分推断（stochastic variational inference）算法，并通过模拟数据与真实数据实验对所提模型进行了验证。