Online Prediction and Learning for Data with Changepoints using Gaussian Processes

Gaussian Processes (GPs) have become an increasingly popular framework for nonlinear regression and learning in a variety of online applications such as control, reinforcement learning, and machine learning. Most GP algorithms assume a static world, and will perform poorly if the generating process switches at discrete instants in time (changepoints). However, many applications of interest, such as controlling an aircraft or predicting the stock market, may include such changepoints. For example, an aircraft may experience actuator failure or the market demand may shift to due a dramatic event. Algorithms which can currently accommodate changepoints currently are limited to batch data or are computationally expensive, making them ill-suited for applications requiring real-time prediction.
 
We have developed a new algorithm for performing prediction and learning with GPs with online data containing changepoints, which overcomes the deficiencies of past approaches. Our algorithm decouples the problems of model learning and changepoint detection using a sparse GP and a nonBayesian hypothesis test for changepoint detection. This results in orders of magnitude speed up over existing methods, allowing for real-time decision making for applications in control and reinforcement learning. Additionally, our method comes with theoretical bounds on the number of samples before the algorithm will successfully detect a changepoint, a property not shared by other methods. This results in extremely robust changepoint detection as well as fast prediction.