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

Abstract

We present the very first robust Bayesian Online Changepoint Detection algorithm through General Bayesian Inference (GBI) with β-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 β→0. Secondly, we give a principled way of choosing the divergence parameter β by minimizing expected predictive loss on-line. We offer the state of the art and improve the False Discovery Rate of CPs by more than 80% on real world data.