Parallel Stochastic Gradient Markov Chain Monte Carlo for Matrix Factorisation Models
This addresses efficient Bayesian inference for large-scale matrix factorisation, offering a scalable solution for practitioners, though it is incremental as it builds on existing SGLD methods.
The paper tackled large matrix factorisation problems by developing a distributed MCMC method called Parallel SGLD (PSGLD), which exploits conditional independence to enable parallelization and achieves high performance with favorable scaling as data size increases, comparable to stochastic gradient descent methods in computational requirements.
For large matrix factorisation problems, we develop a distributed Markov Chain Monte Carlo (MCMC) method based on stochastic gradient Langevin dynamics (SGLD) that we call Parallel SGLD (PSGLD). PSGLD has very favourable scaling properties with increasing data size and is comparable in terms of computational requirements to optimisation methods based on stochastic gradient descent. PSGLD achieves high performance by exploiting the conditional independence structure of the MF models to sub-sample data in a systematic manner as to allow parallelisation and distributed computation. We provide a convergence proof of the algorithm and verify its superior performance on various architectures such as Graphics Processing Units, shared memory multi-core systems and multi-computer clusters.