PLSO: A generative framework for decomposing nonstationary time-series into piecewise stationary oscillatory components

Andrew H. Song, Demba Ba, Emery N. Brown
Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:1371-1381, 2021.

Abstract

To capture the slowly time-varying spectral content of real-world time-series, a common paradigm is to partition the data into approximately stationary intervals and perform inference in the time-frequency domain. However, this approach lacks a corresponding nonstationary time-domain generative model for the entire data and thus, time-domain inference occurs in each interval separately. This results in distortion/discontinuity around interval boundaries and can consequently lead to erroneous inferences based on any quantities derived from the posterior, such as the phase. To address these shortcomings, we propose the Piecewise Locally Stationary Oscillation (PLSO) model for decomposing time-series data with slowly time-varying spectra into several oscillatory, piecewise-stationary processes. PLSO, as a nonstationary time-domain generative model, enables inference on the entire time-series without boundary effects and simultaneously provides a characterization of its time-varying spectral properties. We also propose a novel two-stage inference algorithm that combines Kalman theory and an accelerated proximal gradient algorithm. We demonstrate these points through experiments on simulated data and real neural data from the rat and the human brain.

Cite this Paper

BibTeX
@InProceedings{pmlr-v161-song21a, title = {PLSO: A generative framework for decomposing nonstationary time-series into piecewise stationary oscillatory components}, author = {Song, Andrew H. and Ba, Demba and Brown, Emery N.}, booktitle = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence}, pages = {1371--1381}, year = {2021}, editor = {de Campos, Cassio and Maathuis, Marloes H.}, volume = {161}, series = {Proceedings of Machine Learning Research}, month = {27--30 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v161/song21a/song21a.pdf}, url = {https://proceedings.mlr.press/v161/song21a.html}, abstract = {To capture the slowly time-varying spectral content of real-world time-series, a common paradigm is to partition the data into approximately stationary intervals and perform inference in the time-frequency domain. However, this approach lacks a corresponding nonstationary time-domain generative model for the entire data and thus, time-domain inference occurs in each interval separately. This results in distortion/discontinuity around interval boundaries and can consequently lead to erroneous inferences based on any quantities derived from the posterior, such as the phase. To address these shortcomings, we propose the Piecewise Locally Stationary Oscillation (PLSO) model for decomposing time-series data with slowly time-varying spectra into several oscillatory, piecewise-stationary processes. PLSO, as a nonstationary time-domain generative model, enables inference on the entire time-series without boundary effects and simultaneously provides a characterization of its time-varying spectral properties. We also propose a novel two-stage inference algorithm that combines Kalman theory and an accelerated proximal gradient algorithm. We demonstrate these points through experiments on simulated data and real neural data from the rat and the human brain.} }
Endnote
%0 Conference Paper %T PLSO: A generative framework for decomposing nonstationary time-series into piecewise stationary oscillatory components %A Andrew H. Song %A Demba Ba %A Emery N. Brown %B Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2021 %E Cassio de Campos %E Marloes H. Maathuis %F pmlr-v161-song21a %I PMLR %P 1371--1381 %U https://proceedings.mlr.press/v161/song21a.html %V 161 %X To capture the slowly time-varying spectral content of real-world time-series, a common paradigm is to partition the data into approximately stationary intervals and perform inference in the time-frequency domain. However, this approach lacks a corresponding nonstationary time-domain generative model for the entire data and thus, time-domain inference occurs in each interval separately. This results in distortion/discontinuity around interval boundaries and can consequently lead to erroneous inferences based on any quantities derived from the posterior, such as the phase. To address these shortcomings, we propose the Piecewise Locally Stationary Oscillation (PLSO) model for decomposing time-series data with slowly time-varying spectra into several oscillatory, piecewise-stationary processes. PLSO, as a nonstationary time-domain generative model, enables inference on the entire time-series without boundary effects and simultaneously provides a characterization of its time-varying spectral properties. We also propose a novel two-stage inference algorithm that combines Kalman theory and an accelerated proximal gradient algorithm. We demonstrate these points through experiments on simulated data and real neural data from the rat and the human brain.
APA
Song, A.H., Ba, D. & Brown, E.N.. (2021). PLSO: A generative framework for decomposing nonstationary time-series into piecewise stationary oscillatory components. Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 161:1371-1381 Available from https://proceedings.mlr.press/v161/song21a.html.

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