Online detection of instantaneous changes in the generative process of a data sequence generally focuses on retrospective inference of such change points without considering their future occurrences. We extend the Bayesian Online Change Point Detection algorithm to also infer the number of time steps until the next change point (i.e., the residual time). This enables us to handle observation models which depend on the total segment duration, which is useful to model data sequences with temporal scaling. In addition, we extend the model by removing the i.i.d. assumption on the observation model parameters. The resulting inference algorithm for segment detection can be deployed in an online fashion, and we illustrate applications to synthetic and to two medical real-world data sets.
@cite_0: We combine Bayesian online change point detection with Gaussian processes to create a nonparametric time series model which can handle change points. The model can be used to locate change points in an online manner; and, unlike other Bayesian online change point detection algorithms, is applicable when temporal correlations in a regime are expected. We show three variations on how to apply Gaussian processes in the change point context, each with their own advantages. We present methods to reduce the computational burden of these models and demonstrate it on several real world data sets.
The segmentation and classification of time series has many applications in different fields such as predicting failures in an oil process plant, reconstructing trajectories in air traffic control, the identification of interaction scenarios in robotic environments, real-time brain computer interfaces, probabilistic forecasting of volcano eruptions or forecasting time series with multiple seasonal patterns . For a recent review of change point detection methods we refer to . These models have been especially popular in computer vision for human motion modeling . Regarding the modeling aspect, Gaussian processes have been used to model temporal structure within segments @cite_0 . Alternative methods, which are often based on HMMs, have recently been combined with recurrent and structured inference procedures . In the following, we provide more details about the models we are building on top of: HSMMs and BOCPD, and we point out the differences concerning inference and comment on a setting which leads to a similar generative model.