PLSO: A generative framework for decomposing nonstationary timeseries into piecewise stationary oscillatory components

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, consequently, can 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) generative model for decomposing time-series data with slowly time-varying spectra into several oscillatory, piecewise-stationary processes. PLSO, being a nonstationary time-domain generative model, enables inference on the entire time-series, without boundary effects, and, at the same time, provides a characterization of its time-varying spectral properties. For inference, we propose a novel two-stage algorithm that combines Kalman theory and an accelerated proximal gradient algorithm for the nonconvex objective. We demonstrate these points through experiments on simulated data and real neural data from the rat and the human brain.