Bayesian Online Learning of the Hazard Rate in Change-Point Problems

Change-point models are generative models of time-varying data in which the underlying generative parameters undergo discontinuous changes at different points in time known as change points. Changepoints often represent important events in the underlying processes, like a change in brain state reflected in EEG data or a change in the value of a company reflected in its stock price. However, change-points can be difficult to identify in noisy data streams. Previous attempts to identify change-points online using Bayesian inference relied on specifying in advance the rate at which they occur, called the hazard rate (h). This approach leads to predictions that can depend strongly on the choice of h and is unable to deal optimally with systems in which h is not constant in time. In this letter, we overcome these limitations by developing a hierarchical extension to earlier models. This approach allows h itself to be inferred from the data, which in turn helps to identify when change-points occur. We show that our approach can effectively identify change-points in both toy and real data sets with complex hazard rates and how it can be used as an ideal-observermodel for human and animal behavior when faced with rapidly changing inputs

Sequential Importance Sampling for Online Bayesian Changepoint Detection

Online detection of abrupt changes in the parameters of a generative model for a time series is useful when modelling data in areas of application such as finance, robotics, and biometrics. We present an algorithm based on Sequential Importance Sampling which allows this problem to be solved in an online setting without relying on conjugate priors. Our results are exact and unbiased as we avoid using posterior approximations, and only rely on Monte Carlo integration when computing predictive probabilities. We apply the proposed algorithm to three example data sets. In two of the examples we compare our results to previously published analyses which used conjugate priors. In the third example we demonstrate an application where conjugate priors are not available. Avoiding conjugate priors allows a wider range of models to be considered with Bayesian changepoint detection, and additionally allows the use of arbitrary informative priors to quantify the uncertainty more flexibly