Deep Markov Spatio-Temporal Factorization

We introduce deep Markov spatio-temporal factorization (DMSTF), a deep generative model for spatio-temporal data. Like other factor analysis methods, DMSTF 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 we infer using stochastic variational inference. The innovation in DMSTF is that we parameterize weights in terms of a deep Markovian prior, which is able to characterize nonlinear temporal dynamics. We parameterize the corresponding variational distribution using a bidirectional recurrent network. This results in a flexible family of hierarchical deep generative factor analysis models that can be extended to perform time series clustering, or perform factor analysis in the presence of a control signal. Our experiments, which consider simulated data, fMRI data, and traffic data, demonstrate that DMSTF outperforms related methods in terms of reconstruction accuracy and can perform forecasting in a variety domains with nonlinear temporal transitions.