Generalised Latent Slice Sampling

Kirill Tamogashev, Sanghyeok Choi, Arran Carter, Víctor Elvira, alix, Esmeralda S. Whitammer

Keywords: Slice Sampling, Monte Carlo, MCMC, Sampling, Parallel Tempering, Bayesian Inference

TL;DR: We generalise latent slice sampling to make it more efficient for high-dimensional distributions and combine it with replica-exchange methods.

Abstract:

Slice sampling is a family of auxiliary-variable Monte Carlo
algorithms that convert the problem of sampling from a target
distribution to one of sampling from the region bounded by the
graph of its density function. The main challenge in implementing
slice samplers is performing constrained resampling from the region
where the density exceeds a threshold, which typically involves
selecting a search region -- by a stepping-out or probabilistic
procedure -- and then applying a shrinkage algorithm until a point
within the slice is found. Here, we generalise a probabilistic
method for selecting the search region to select ellipsoids instead
of hyperrectangles and introduce efficient shrinkage and adaptation
procedures. We also show for the first time that slice sampling can
be combined with parallel tempering to improve performance on
multi-modal targets. All new algorithms are implemented efficiently
in vectorised form and benchmarked on some target distributions,
where the proposed methods show improvement in sample-based metrics as a function of the number of target evaluations compared to prior methods.

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Submission Number: 78