Deconvolution of mixing time series on a graph

Alexander W. Blocker, Edoardo M. Airoldi
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:68-88, 2011.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-blocker11a, title = {Deconvolution of mixing time series on a graph}, author = {Blocker, Alexander W. and Airoldi, Edoardo M.}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {68--88}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/blocker11a/blocker11a.pdf}, url = {https://proceedings.mlr.press/r9/blocker11a.html}, 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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Deconvolution of mixing time series on a graph %A Alexander W. Blocker %A Edoardo M. Airoldi %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-blocker11a %I PMLR %P 68--88 %U https://proceedings.mlr.press/r9/blocker11a.html %V R9 %X 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. %Z Reissued by PMLR on 04 October 2026.
APA
Blocker, A.W. & Airoldi, E.M.. (2011). Deconvolution of mixing time series on a graph. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:68-88 Available from https://proceedings.mlr.press/r9/blocker11a.html. Reissued by PMLR on 04 October 2026.

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