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

TL;DR

The paper introduces PLSO, a nonstationary generative model that decomposes time-series into piecewise stationary oscillations, enabling boundary-free inference and characterization of time-varying spectra, demonstrated on neural data.

Contribution

It proposes the PLSO model for nonstationary time-series decomposition and a novel inference algorithm combining Kalman theory and proximal gradient methods.

Findings

Effective decomposition of neural signals into oscillatory components.

Boundary effects are eliminated in the proposed model.

Model accurately captures time-varying spectral properties.

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.