

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 inter-dependencies 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 {#sec:intro}
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Background and Motivation {#sec:Backg}
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Problem Formulation: Deep Switching Auto-Regressive Factorization {#sec:prob}
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Experimental Evaluation {#sec:experimental}
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Conclusion
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\[sec:conclu\]

Ethics Statement {#ethics-statement .unnumbered}
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The model we proposed in this work is a step toward better understanding of high dimensional time series data that appear in a variety of real-world settings. Analysing and more importantly *forecasting* these times series naturally embrace a very broad range of applications from healthcare management, disease spread prediction and infection diagnosis to traffic control and weather and financial forecasting, which are where we see the potential for a broader impact. Although, these time series data often show long- and short-term recurring patterns, they occasionally exhibit sophisticated behaviours or are chaotic. Subsequently, we need appropriate tools and legitimate assumptions for analysing them. While we understand that, as George Box wrote in @box1979robustness, "all models are wrong but some are useful," we hope that in a wide range of applications with proper assumptions and prior knowledge, our DSARF model be useful in providing a means to analyzing high dimensional spatio-temporal data.

[^1]: The source code and experiments are provided as part of the supplementary submission.

{'source': 'arXiv_out/2009'}