🤖 AI Summary
This work proposes the Automatic Slice Gibbs (ASG) framework to address the challenge of efficiently sampling from non-standardized, non-smooth, heavy-tailed, and highly multimodal distributions. ASG combines a Cauchy transformation to adaptively estimate the effective support set and employs slice-driven Gibbs updates to enable fully automatic Markov chain Monte Carlo (MCMC) sampling—requiring no user-specified truncation bounds, proposal scales, geometric priors, or gradient information. The method automatically handles disconnected high-density regions and complex geometric structures. Empirical evaluations on Beta mixtures, Rosenbrock, Ackley, and non-smooth LASSO-type posteriors demonstrate that ASG consistently achieves substantially higher effective sample sizes per unit time and faster decorrelation compared to random-walk Metropolis–Hastings, adaptive Gibbs samplers, and other slice sampling approaches.
📝 Abstract
An Automated Sliced Gibbs framework is proposed for fully automated Markov chain Monte Carlo sampling from arbitrary finite dimensional probability kernels. The method targets unnormalized, non-smooth, heavy tailed, and highly multimodal densities. A Cauchy transformation based effective support estimator is combined with slice driven Gibbs updates. This construction removes the need for user specified truncation bounds, proposal scales, step-size tuning, or conditional optimization. Unlike existing slice samplers, ASG does not require manually chosen bracket widths or geometric insight into the support. All calibration is performed automatically within each Gibbs cycle. The resulting Markov chain preserves invariance and ergodicity. Automated support detection allows efficient movement across disconnected high density regions. The sampler adapts to sharp curvature and irregular geometry without gradient information. Extensive numerical experiments evaluate performance on complex kernels, including univariate Beta mixtures, multivariate Rosenbrock and Ackley benchmarks, and non-smooth kernels derived from generalized LASSO type loss functions. Across these challenging settings, ASG consistently achieves higher effective sample size per second and faster decorrelation than Random Walk Metropolis Hastings, adaptive Gibbs variants, and some recently proposed slice based methods. The framework provides a scalable and general-purpose solution for sampling from complicated probability kernels where existing algorithms require substantial tuning or exhibit slow mixing.