Bayesian Online Change Point Detection with Hilbert Space Approximate Student-T Process

Abstract

In this paper, we introduce a variant of Bayesian online change point detection with a reducedrank Student-t process (TP) and dependent Student-t noise, as a nonparametric time series model. Our method builds and improves upon the state-of-the-art Gaussian process (GP) change point model benchmark of Saatci et al. (2010). The Student-t process generalizes the concept of a GP and hence yields a more flexible alternative. Additionally, unlike a GP, the predictive variance explicitly depends on the training observations, while the use of an entangled Student-t noise model preserves analytical tractability. Our approach also uses a Hilbert space reduced-rank representation of the TP kernel, derived from an eigenfunction expansion of the Laplace operator (Solin & Sarkka, 2020), to alleviate its computational complexity. Improvements in prediction and training time are demonstrated with real-world data-sets