Matrix factorization is a very common machine learning technique in recommender systems. Bayesian Matrix Factorization (BMF) algorithms would be attractive because of their ability to quantify uncertainty in their predictions and avoid over-fitting, combined with high prediction accuracy. However, they have not been widely used on large-scale data because of their prohibitive computational cost. In recent work, efforts have been made to reduce the cost, both by improving the scalability of the BMF algorithm as well as its implementation, but so far mainly separately. In this paper we show that the state-of-the-art of both approaches to scalability can be combined. We combine the recent highly-scalable Posterior Propagation algorithm for BMF, which parallelizes computation of blocks of the matrix, with a distributed BMF implementation that users asynchronous communication within each block. We show that the combination of the two methods gives substantial improvements in the scalability of BMF on web-scale datasets, when the goal is to reduce the wall-clock time.
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