Sticky PDMP samplers for sparse and local inference problems

Abstract

We construct a new class of efficient Monte Carlo methods based on continuous-time piecewise deterministic Markov processes (PDMPs) suitable for inference in high dimensional sparse models, i.e. models for which there is prior knowledge that many coordinates are likely to be exactly $0$. This is achieved with the fairly simple idea of endowing existing PDMP samplers with 'sticky' coordinate axes, coordinate planes etc. Upon hitting those subspaces, an event is triggered during which the process sticks to the subspace, this way spending some time in a sub-model. This results in non-reversible jumps between different (sub-)models. While we show that PDMP samplers in general can be made sticky, we mainly focus on the Zig-Zag sampler. Compared to the Gibbs sampler for variable selection, we heuristically derive favourable dependence of the Sticky Zig-Zag sampler on dimension and data size. The computational efficiency of the Sticky Zig-Zag sampler is further established through numerical experiments where both the sample size and the dimension of the parameter space are large.

arXiv comment43 pages, 13 figures

References in corpus (5)

• Spike and slab variable selection: Frequentist and Bayesian strategies
• Bayesian variable selection regression for genome-wide association studies and other large-scale problems
• The Zig-Zag Process and Super-Efficient Sampling for Bayesian Analysis of Big Data
• Ergodicity of the zigzag process
• Scalable Importance Tempering and Bayesian Variable Selection

Cited by in corpus (1)

• Piecewise deterministic sampling with splitting schemes