Periodic Gaussian Process Controlled B-Spline for Scalable Modeling of Irregularly Spaced Signals

Existing periodic Gaussian process (PGP) modeling methods rely on the regularly-spaced-signal assumption (i.e., signals are evenly spaced) and the integer-period assumption for the sake of computational feasibility. However, such an assumption prevents conventional efficient modeling approaches from working properly on irregularly (unevenly) spaced signals, such as evenly spaced signals with missing data. Moreover, without the integer-period assumption, it is computationally prohibitive to accurately search the decimal period of PGP due to the severe non-convexity of its likelihood function. To address these issues, this study proposes a PGP-controlled B-spline for scalable modeling of irregularly spaced signals with a decimal period. The proposed model integrates PGP with B-spline basis functions, allowing for nonlinear and nonparametric modeling of periodic signals. An explore-exploit optimization is developed to overcome the non-convexity of the likelihood, enabling effective and efficient decimal period estimation. The proposed PGP modeling approach has a linear time complexity. Asymptotic properties of the proposed method are studied, which shed light on the period estimation of other PGP models. Simulation and real case studies are conducted to demonstrate the superiority of the proposed method.