Streaming Bayesian inference: theoretical limits and mini-batch approximate message-passing


In statistical learning for real-world large-scale data problems, one must often resort to “streaming” algorithms which operate sequentially on small batches of data. In this work, we present an analysis of the information-theoretic limits of mini-batch inference in the context of generalized linear models and low-rank matrix factorization. In a controlled Bayes-optimal setting, we characterize the optimal performance and phase transitions as a function of mini-batch size. We base part of our results on a detailed analysis of a mini-batch version of the approximate message-passing algorithm (Mini-AMP), which we introduce. Additionally, we show that this theoretical optimality carries over into real-data problems by illustrating that Mini-AMP is competitive with standard streaming algorithms for clustering.

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@article{Manoel2017StreamingBI, title={Streaming Bayesian inference: theoretical limits and mini-batch approximate message-passing}, author={Andre Manoel and Florent Krzakala and Eric W. Tramel and Lenka Zdeborov{\'a}}, journal={CoRR}, year={2017}, volume={abs/1706.00705} }