Change Detection and Gaussian Process Inference in Piecewise Stationary Environments under Noisy Inputs

Gaussian Process (GP) inference in dynamical piecewise stationary environments finds application in many modern real-world problems. Here we focus on scenarios in which precise initial training data is available but each subsequent measurement is taken with uncertainty with respect to the location at which it was taken. In such a scenario, the ideal inference methodology should update the GP only if a considerable change occurs. Furthermore, the update strategy should preserve 'correct' initial information in unchanged regions. In this contribution, we propose a change detection methodology which operates in conjunction with the inference process. The proposed detection method is based on the Kolmogorov-Smirnov statistics in such way that an exact PDF can be derived under the null hypothesis. Once detection has occurred, the GP can be naively updated by replacing appropriate measurements in the data set by an average computed from the new, noisy samples. Simulations with synthetic data provide a proof of concept of the proposed strategy as well as its robustness to noisy inputs.