Doubly Robust Bayesian Inference For Non-Stationary Streaming Data With $\beta$-Divergences

Authors:
Jeremias Knoblauch Warwick University
Jack E Jewson University of Warwick
Theo Damoulas University of Warwick The Alan Turing Institute

Introduction:

The authors present the very first robust Bayesian Online Changepoint Detection algorithm through General Bayesian Inference (GBI) with $eta$-divergences.

Abstract:

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. Reducing False Discovery Rates of \CPs from up to 99\% to 0\% on real world data, this offers the state of the art.

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