title: Deconvolution of mixing time series on a graph.
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,yt=Axt, where the projection mechanism provides information onA. We consider problems in whichAspecifies 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 multivariate time series.
authors.affiliation: Department of Statistics Harvard University Cambridge, MA 02138.
authors.forename: Alexander W
authors.initials: AW
authors.lastname: Blocker
authors.affiliation: Department of Statistics Harvard University Cambridge, MA 02138.
authors.forename: Edoardo M
authors.initials: EM
authors.lastname: Airoldi