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

arXiv: https://arxiv.org/abs/1806.02261 · HTML: https://mlsanity.com/paper/1806.02261/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2018.

## Built on by (most cited first, 21 of 21)

- [A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methods](https://mlsanity.com/paper/2305.15027/) (2023)
- [Outlier-robust Kalman Filtering through Generalised Bayes](https://mlsanity.com/paper/2405.05646/) (2024)
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- [Robust and Conjugate Gaussian Process Regression](https://mlsanity.com/paper/2311.00463/) (2023)
- [WATCH: Wasserstein Change Point Detection for High-Dimensional Time Series Data](https://mlsanity.com/paper/2201.07125/) (2022)
- [Detecting Rumours with Latency Guarantees using Massive Streaming Data](https://mlsanity.com/paper/2205.06580/) (2022)
- [Open problems in causal structure learning: A case study of COVID-19 in the UK](https://mlsanity.com/paper/2305.03859/) (2023)
- [MOSPAT: AutoML based Model Selection and Parameter Tuning for Time Series Anomaly Detection](https://mlsanity.com/paper/2205.11755/) (2022)
- [Active multi-fidelity Bayesian online changepoint detection](https://mlsanity.com/paper/2103.14224/) (2021)
- [A unifying framework for generalised Bayesian online learning in non-stationary environments](https://mlsanity.com/paper/2411.10153/) (2024)
- [Alpha-VI DeepONet: A prior-robust variational Bayesian approach for enhancing DeepONets with uncertainty quantification](https://mlsanity.com/paper/2408.00681/) (2024)
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- [Unsupervised Change Detection using DRE-CUSUM](https://mlsanity.com/paper/2201.11678/) (2022)
- [Differentially Private Statistical Inference through β-Divergence One Posterior Sampling](https://mlsanity.com/paper/2307.05194/) (2023)
- [Federated Generalised Variational Inference: A Robust Probabilistic Federated Learning Framework](https://mlsanity.com/paper/2502.00846/) (2025)
- [Robust Bayesian Optimisation with Unbounded Corruptions](https://mlsanity.com/paper/2511.15315/) (2025)
- [Generalized Bayes for Causal Inference](https://mlsanity.com/paper/2603.03035/) (2026)
- [Greedy online change point detection](https://mlsanity.com/paper/2308.07012/) (2023)
- [On the meaning of uncertainty for ethical AI: philosophy and practice](https://mlsanity.com/paper/2309.05529/) (2023)
- [Active Learning for Multiple Change Point Detection in Non-stationary Time Series with Deep Gaussian Processes](https://mlsanity.com/paper/2505.20452/) (2025)
- [High-Dimensional Online Change Point Detection with Adaptive Thresholding and Interpretability](https://mlsanity.com/paper/2609.24278/) (2026)

## Abstract (arXiv)

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 → 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.