Deep Switching Auto-Regressive Factorization: Application to Time Series Forecasting

We introduce deep switching auto-regressive factorization (DSARF), a deep generative model for spatio-temporal data with the capability to unravel recurring patterns in the data and perform robust short-and long-term predictions. Similar to other factor analysis methods, DSARF approximates high dimensional data by a product between time dependent weights and spatially dependent factors. These weights and factors are in turn represented in terms of lower dimensional latent variables that are inferred using stochastic variational inference. DSARF is different from the state-of-the-art techniques in that it parameterizes the weights in terms of a deep switching vector auto-regressive likelihood governed with a Markovian prior, which is able to capture the non-linear interdependencies among weights to characterize multimodal temporal dynamics. This results in a flexible hierarchical deep generative factor analysis model that can be extended to (i) provide a collection of potentially interpretable states abstracted from the process dynamics, and (ii) perform short-and long-term vector time series prediction in a complex multi-relational setting. Our extensive experiments, which include simulated data and real data from a wide range of applications such as climate change, weather forecasting, traffic, infectious disease spread and nonlinear physical systems attest the superior performance of DSARF in terms of long-and short-term prediction error, when compared with the state-of-the-art methods 1 . Introduction Ever-improving sensing technologies offer fast and accurate collection of large-scale spatio-temporal data in various applications, ranging from medicine and biology to marketing and traffic control. In these domains, modeling the temporal dynamics and spatial relations of data have been investigated and analysed from different perspectives. As these multivariate spatio-temporal data often exhibit high levels of correlation between dimensions, they can naturally be thought of as governed by a smaller number of underlying components. Tensor/matrix factorization frameworks are used to describe variability in these correlated