Spatio-Temporal Random Fields

Modern sensing technology allows us enhanced monitoring of dynamic activities in various domains. The increasing amount of sensor measurements, however, brings us the challenge for efficient data analysis. This is especially true when sensing targets can interoperate—in such cases we need learning models that can capture the relations of sensors, possibly without collecting or exchanging all data. Generative graphical models namely the Markov random fields (MRFs) fit this purpose, which can represent complex spatial and temporal relations among sensors, producing interpretable answers in terms of probability. The only drawback will be the cost for inference, storing and optimizing a very large number of parameters — not uncommon when we apply them for real-world applications. In this paper, we investigate how we can make discrete probabilistic graphical models practical for predicting sensor states in a spatio-temporal setting. A set of new ideas allows keeping the advantages of such models while achieving scalability. We first introduce a novel alternative to represent model parameters, which enables us to compress the parameter storage by removing uninformative parameters in a systematic way. For finding the best parameters via approximate maximum likelihood estimation, we provide a separable optimization algorithm that can be performed independently in parallel in each graph node. We illustrate that the prediction quality of our suggested methods is comparable to those of the standard MRFs and a spatio-temporal k-nearest neighbor method, while using much less computational resources.

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