An Efficient Minibatch Acceptance Test for Metropolis-Hastings
This addresses the problem of slow Bayesian inference for practitioners dealing with big data, though it appears incremental as it builds on existing noise-tolerant tests.
The paper tackles the computational cost of Metropolis-Hastings sampling on large datasets by introducing a method that uses small minibatches with an adjustable batch size, achieving several order-of-magnitude speedups over prior work.
We present a novel Metropolis-Hastings method for large datasets that uses small expected-size minibatches of data. Previous work on reducing the cost of Metropolis-Hastings tests yield variable data consumed per sample, with only constant factor reductions versus using the full dataset for each sample. Here we present a method that can be tuned to provide arbitrarily small batch sizes, by adjusting either proposal step size or temperature. Our test uses the noise-tolerant Barker acceptance test with a novel additive correction variable. The resulting test has similar cost to a normal SGD update. Our experiments demonstrate several order-of-magnitude speedups over previous work.