Doubly Robust Bayesian Inference for Non-Stationary Streaming Data with $β$-Divergences
This provides a robust solution for detecting changepoints in streaming data, which is crucial for applications like financial monitoring or sensor networks, though it builds incrementally on existing Bayesian methods.
The authors tackled the problem of robust Bayesian online changepoint detection for non-stationary streaming data, achieving a reduction in false discovery rates from over 90% to 0% on real-world data with linear time and constant space complexity.
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 parameter 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 $β\to 0$. Secondly, we give a principled way of choosing the divergence parameter $β$ by minimizing expected predictive loss on-line. Reducing False Discovery Rates of CPs from more than 90% to 0% on real world data, this offers the state of the art.