Doubly Robust Bayesian Inference for Non-Stationary Streaming Data with \beta -Divergences

We present the very first robust Bayesian Online Changepoint Detection algorithm through General Bayesian Inference (GBI) with \beta -divergences. The resulting inference procedure is doubly robust for both the predictive and the changepoint (CP) posterior, with linear time and constant space complexity. We provide a construction for exponential models and demonstrate it on the Bayesian Linear Regression model. In so doing, we make two additional contributions: Firstly, we make GBI scalable using Structural Variational approximations that are exact as \beta \to 0 . Secondly, we give a principled way of choosing the divergence parameter \beta by minimizing expected predictive loss on-line.