Adaptive Sequential Bayesian Change Point Detection
Ryan Turner, Yunus Saatci and Carl Edward Rasmussen
In: Temporal Segmentation Workshop at NIPS 2009, 12 Dec 2009, Whistler, BC.
Real-world time series are often nonstationary with respect to the
parameters of some underlying prediction model (UPM). Furthermore,
it is often desirable to adapt the UPM to incoming regime changes
as soon as possible, necessitating sequential inference about change
point locations. A Bayesian algorithm for online change point detection
(BOCPD) has been introduced recently by Adams and MacKay (2007).
In this algorithm, uncertainty about the last change point location
is updated sequentially, and is integrated out to make online predictions
robust to parameter changes. BOCPD requires a set of fixed hyper-parameters
which allow the user to fully specify the hazard function for change
points and the prior distribution over the parameters of the UPM.
In practice, finding the ``right'' hyper-parameters can be quite
difficult. We therefore extend BOCPD by introducing hyper-parameter
learning, without sacrificing the online nature of the algorithm.
Hyper-parameter learning is performed by optimizing the marginal
likelihood of the BOCPD model, a closed-form quantity which can be
computed sequentially. We illustrate performance on three real-world