EXPLICIT LINK BETWEEN PERIODIC COVARIANCE FUNCTIONS AND STATE SPACE MODELS
Arno Solin, Simo Särkkä · 2014
This paper shows how periodic covariance functions in Gaussian process regression can be reformulated as state space models, which can be solved with classical Kalman filter-ing theory. This reduces the problematic cu-bic complexity of Gaussian process regression in the number of time steps into linear time complexity. The representation is based on expanding periodic covariance functions into a series of stochastic resonators. The explicit representation of the canonical periodic co-variance function is written out and the ex-pansion is shown to uniformly converge to the exact covariance function with a known convergence rate. The framework is gener-alized to quasi-periodic covariance functions by introducing damping terms in the system and applied to two sets of real data. The approach could be easily extended to non-stationary and spatio-temporal variants. 1