Generative Modeling of Approximately Periodic Time Series by a Posterior-Weighted Gaussian Process
For practitioners modeling industrial or cyber-physical processes with repetitive but variable patterns, this offers a generative model that captures both regularity and variability.
The paper tackles generative modeling of approximately periodic time series, where repetitions vary in duration, amplitude, and dynamics. It proposes a posterior-weighted Gaussian Process that decouples intra- and inter-repetition variability, generating realistic synthetic trajectories from toy datasets.
Discrete automated processes in industrial and cyber-physical systems often exhibit a repetitive structure in which successive repetitions follow a common trajectory while differing in duration, amplitude, and fine-scale dynamics. Such \emph{approximately periodic} behavior poses a challenge for Gaussian Processes (GP) modeling: strictly periodic models suppress inter-repetition variability, while non-periodic models fail to capture the strong structural regularities required for generation. In this work, we propose a stochastic generative model for approximately periodic time series. The model is based on a GP whose posterior is modulated by a novel kernel. Our approach decouples intra-repetition structure from inter-repetition variability through a two-stage construction which yields a generative distribution with a identical mean function across repetitions, while allowing smooth variation between repetitions. The modeling choices are supported by an implementation in which realistic synthetic trajectories are generated from toy datasets.