Computationally efficient Gaussian Process changepoint detection and regression
Robert C. Grande · DSpace@MIT (Massachusetts Institute of Technology) · 2014
Most existing GP regression algorithms assume a single generative model, leading to poor performance when data are nonstationary, i.e. generated from multiple switching processes. Existing methods for GP regression over non-stationary data include clustering and change-point detection algorithms. However, these methods require significant computation, do not come with provable guarantees on correctness and speed, and most algorithms only work in batch settings. This thesis presents an efficient online GP framework, GP-NBC, that leverages the generalized likelihood ratio test to detect changepoints and learn multiple Gaussian Process models from streaming data. Furthermore, GP-NBC can quickly recog-nize and reuse previously seen models. The algorithm is shown to be theoretically sample efficient in terms of limiting mistaken predictions. Our empirical results on two real-world datasets and one synthetic dataset show GP-NBC outperforms state of the art methods for nonstationary regression in terms of regression error and computational efficiency. The second part of the thesis introduces a Reinforcement Learning (RL) algorithm, UCRL-GP-CPD, for multi-task Reinforcement Learning when the reward function is non-