Gaussian Process Change Point Models

•Combine Bayesian change point detection with Gaussian Processes to define a nonstationary time series model. •Central aim is to react to underlying regime changes in an online manner. •Able to integrate out all latent variables and optimize hyperparameters sequentially. •Explore three alternative ways of augmenting GP models to handle nonstationarity (GPTS, ARGPCP and NSGP – see below). •A Bayesian approach (BOCPD) for online change point detection was introduced in [1]. •BOCPD introduces a latent variable representing the run length at time t and adapts predictions via integrating out the run length. •BOCPD has two key ingredients: –Any model which can construct a predictive density for future observations, in particular, p(xt|x(t−τ ):(t−1), θm), i.e., the “underlying predictive model” (UPM). –A hazard function H(r|θh) which encodes our prior belief in a change point occuring after observing a run length r.