Deconvolution of mixing time series on a graph

Alexander W. Blocker; Edoardo M. Airoldi

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arXiv · 1105.2526

Deconvolution of mixing time series on a graph

Alexander W. Blocker·Edoardo M. Airoldi

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Abstract

In many applications we are interested in making inference on latent time series from indirect measurements, which are often low-dimensional projections resulting from mixing or aggregation. Positron emission tomography, super-resolution, and network traffic monitoring are some examples. Inference in such settings requires solving a sequence of ill-posed inverse problems, y_t= A x_t, where the projection mechanism provides information on A. We consider problems in which A specifies mixing on a graph of times series that are bursty and sparse. We develop a multilevel state-space model for mixing times series and an efficient approach to inference. A simple model is used to calibrate regularization parameters that lead to efficient inference in the multilevel state-space model. We apply this method to the problem of estimating point-to-point traffic flows on a network from aggregate measurements. Our solution outperforms existing methods for this problem, and our two-stage approach suggests an efficient inference strategy for multilevel models of dependent time series.

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Alexander W. Blocker, Edoardo M. Airoldi. 2011-06-10. Deconvolution of mixing time series on a graph. https://arxiv.org/abs/1105.2526

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