Bayesian matrix factorization (BMF) is a powerful tool for producing low-rank representations of matrices, and giving principled predictions of missing values. However, scaling up MCMC samplers to large matrices has proven to be difficult with parallel algorithms that require communication between MCMC iterations. On the other hand, designing communication-free algorithms is challenging due to the inherent unidentifiability of BMF solutions. We propose posterior propagation, an embarrassingly parallel inference procedure, which hierarchically introduces dependencies between data subsets and thus alleviates the unidentifiability problem.
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