Generative Modeling of Approximately Periodic Time Series by a Posterior-Weighted Gaussian Process

• URL: http://arxiv.org/abs/2605.13150v1
• Date: Wed, 13 May 2026 08:17:00 GMT
• Title: Generative Modeling of Approximately Periodic Time Series by a Posterior-Weighted Gaussian Process
• Abstract summary: We propose a generative model for approximately periodic time series.<n>Our approach decouples intra-repetition structure from inter-repetition variability through a two-stage construction.
• Score: 0.4460583138505672
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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