Improving efficiency of slice sampling by tuning search steps automatically
Optimal Slice-Adaptive Tuning of Hybrid Slice Sampling
Machine Learning
Summary
Slice sampling is a way for computers to explore complicated landscapes to make guesses about patterns or probabilities. It involves choosing a random slice or interval where the answer might lie, but since the exact slice isn’t known, people start with a guess size and adjust it. The authors study how the size of these initial guesses affects how many times the computer checks its target. They develop smart methods that automatically tune this size for faster, efficient searching, and tests show these methods work well without needing careful initial settings.
slice samplingMarkov chain Monte Carlotarget densitysuper-level setinterval tuninghybrid slice samplingdensity evaluationautomated tuningconvergence guaranteescomputational efficiency
Authors
Trevor Campbell
Abstract
Slice sampling is a Markov chain Monte Carlo algorithm that draws its next state uniformly from a "slice"---a super-level set of the target density function---at each iteration, thereby providing automatic local adaptivity to the scale of the target. In practice the exact slice is not known, so general-purpose implementations use an approximate slice that is grown from a starting interval of length $w>0$, with a computational cost that depends on $w$. This work presents an analysis of the average per-iteration number of target density evaluations, as a function of $w$, of hybrid slice sampling with various slice-finding schemes for targets with contiguous slices. The paper uses the results of the analysis to develop automated, slice-adaptive tuning schemes along with suboptimality bounds and asymptotic convergence guarantees. Simulations demonstrate that the tuning schemes reliably yield near-optimal slice-adaptive tuning with essentially no dependence on the initial setting of $w$.