Communication-Aware MCMC Method for Big Data Applications on FPGAs

Markov Chain Monte Carlo (MCMC) based methods have been the main tool for Bayesian Inference for some years now, and recently they find increasing applications in modern statistics and machine learning. Nevertheless, with the availability of large datasets and increasing complexity of Bayesian models, MCMC methods are becoming prohibitively expensive for real-world problems. At the heart of these methods, lies the computation of likelihood functions that requires access to all input data points in each iteration of the method. Current approaches, based on data subsampling, aim to accelerate these algorithms by reducing the number of the data points for likelihood evaluations at each MCMC iteration. However the existing work doesn't consider the properties of modern memory hierarchies, but treats the memory as one monolithic storage space. This paper proposes a communication-aware MCMC framework that takes into account the underlying performance of the memory subsystem. The framework is based on a novel subsampling algorithm that utilises an unbiased likelihood estimator based on Probability Proportional-to-Size (PPS) sampling, allowing information on the performance of the memory system to be taken into account during the sampling stage. The proposed MCMC sampler is mapped to an FPGA device and its performance is evaluated using the Bayesian logistic regression model on MNIST dataset. The proposed system achieves a 3.37x speed up over a highly optimised traditional FPGA design, therefore the risk in the estimates based on the generated samples is largely decreased.