Fast Compression of MCMC Output

We propose cube thinning, a novel method for compressing the output of an MCMC (Markov chain Monte Carlo) algorithm when control variates are available. It allows resampling of the initial MCMC sample (according to weights derived from control variates), while imposing equality constraints on the averages of these control variates, using the cube method (an approach that originates from survey sampling). The main advantage of cube thinning is that its complexity does not depend on the size of the compressed sample. This compares favourably to previous methods, such as Stein thinning, the complexity of which is quadratic in that quantity.

Automated summary

Cube thinning is a novel method for compressing the output of an MCMC algorithm with control variates, allowing for resampling of the initial sample based on weights derived from the control variates. The advantage of cube thinning is that its complexity is independent of the size of the compressed sample, unlike previous methods such as Stein thinning.