A Mixture-of-Experts Framework for Multi-Stream Quickest Change Detection

A Mixture-of-Experts (MoE) framework is proposed for quickest change detection (QCD) where there are multiple experts, and each expert produces a sequence of statistics for change detection. A change is declared when a weighted sum of these statistics crosses a threshold. This framework is then applied to the problem of multi-stream QCD to obtain a family of powerful algorithms that outperform the best known algorithms in the literature. In the multi-stream QCD problem, a decision-maker observes multiple streams of observations. At the change point, the distribution of an unknown subset of the streams changes. The optimal algorithm based on a generalized likelihood ratio is computationally expensive. One of the most computationally and performance-efficient algorithms in the literature is the rank-weighted sum (RWS) scheme based on Shiryaev-Roberts statistics. It is shown in the paper that the MoE-based QCD algorithm for multi-stream data outperforms the RWS scheme. This is demonstrated through simulation results on real-valued Gaussian mean shift data and high-dimensional data from Gaussian--Bernoulli Restricted Boltzmann Machines (GB-RBMs).