Generative Modeling of Approximately Periodic Time Series by a Posterior-Weighted Gaussian Process
Authors: Elias Reich, Saverio Messineo, Stefan Huber
Summary
arXiv:2605. 13150v1 Announce Type: new 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.
Relevance
Read next because Generative Modeling of Approximately Periodic Time Series by a Posterior-Weighted Gaussian Process overlaps with clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "Coupling evil personas with wrong answers fails to protect Qwen2.5-7B from EM-induced alignment collapse — and the apparent capability ordering across coupling conditions is mostly eval contamination (LOW confidence)", clean result "Only continuous soft prefixes hit both EM axes at once on Qwen-2.5-7B-Instruct: discrete prompt searches split between the alignment objective and the distributional objective, and both discretizations of the soft prefix collapse (MODERATE confidence)". Matching terms: strong, rate, model, discrete. Source: arxiv stat.ML (Machine Learning).
Abstract
arXiv:2605.13150v1 Announce Type: new 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.