Gibberd, AJ;
Nelson, JDB;
(2015)
Estimating multiresolution dependency graphs within the stationary wavelet framework.
In:
Proceedings of the 2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP).
(pp. pp. 547-551).
IEEE: Orlando, FL, USA.
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Abstract
Very recently, the locally stationary wavelet framework has provided a means to describe the dependencies of co-varying time-series over a range of multiple scale levels. However, describing the many interactions between data-streams at different scale levels with only finite data poses some serious statistical estimation challenges. We illustrate that existing approaches suffer from large variance and are sometimes difficult to interpret. We here propose a sparsity-aware estimator which furnishes a set of multiresolution, dynamic graphs that describe how the dependency structure of the variables evolves through time and over multiple levels of scale. We show that the regulariser mitigates the variance and that, since the inference is performed using convex optimisation, it converges quickly to a global optima and scales well with respect to samples and nodes. Basic properties of the new method are established on simulated data. The method is applied to inferring dependency structure in multivariate EEG data-sets during epileptic seizures where it reveals evidence of band-limited dependency structure.
| Type: | Proceedings paper |
|---|---|
| Title: | Estimating multiresolution dependency graphs within the stationary wavelet framework |
| Event: | 2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP) |
| ISBN-13: | 9781479975914 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/GlobalSIP.2015.7418255 |
| Publisher version: | http://dx.doi.org/10.1109/GlobalSIP.2015.7418255 |
| Language: | English |
| Additional information: | Copyright © 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. |
| Keywords: | Coherence, Covariance matrices, Estimation, Graphical models, Signal processing, Sparse matrices, Wavelet transforms |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1477556 |
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