# Distributed Bayesian Matrix Factorization with Limited Communication

## TL;DR

This paper presents a hierarchical Bayesian matrix factorization method that enables efficient distributed inference with minimal communication, significantly speeding up computation while maintaining high accuracy.

## Contribution

It introduces a hierarchical decomposition of the joint posterior, allowing embarrassingly parallel inference in a few stages, improving scalability and efficiency.

## Key findings

- Achieves nearly tenfold speed-up over full posterior inference.
- Maintains negligible loss in predictive accuracy.
- Outperforms existing embarrassingly parallel MCMC methods.

## Abstract

Bayesian matrix factorization (BMF) is a powerful tool for producing low-rank representations of matrices and for predicting missing values and providing confidence intervals. Scaling up the posterior inference for massive-scale matrices is challenging and requires distributing both data and computation over many workers, making communication the main computational bottleneck. Embarrassingly parallel inference would remove the communication needed, by using completely independent computations on different data subsets, but it suffers from the inherent unidentifiability of BMF solutions. We introduce a hierarchical decomposition of the joint posterior distribution, which couples the subset inferences, allowing for embarrassingly parallel computations in a sequence of at most three stages. Using an efficient approximate implementation, we show improvements empirically on both real and simulated data. Our distributed approach is able to achieve a speed-up of almost an order of magnitude over the full posterior, with a negligible effect on predictive accuracy. Our method outperforms state-of-the-art embarrassingly parallel MCMC methods in accuracy, and achieves results competitive to other available distributed and parallel implementations of BMF.