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

arXiv: https://arxiv.org/abs/1706.00705 · HTML: https://mlsanity.com/paper/1706.00705/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2017.

## Built on by (most cited first, 3 of 3)

- [Deep learning via message passing algorithms based on belief propagation](https://mlsanity.com/paper/2110.14583/) (2021)
- [Bayesian reconstruction of memories stored in neural networks from their connectivity](https://mlsanity.com/paper/2105.07416/) (2021)
- [Streaming Belief Propagation for Community Detection](https://mlsanity.com/paper/2106.04805/) (2021)

## Abstract (arXiv)

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.