Sticky PDMP samplers for sparse and local inference problems
Journal article, 2023

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.

Spike-and-slab

High-dimensional problems

Big-data

Bayesian variable selection

Piecewise deterministic Markov process

Monte Carlo

Non-reversible jump

Author

Joris Bierkens

Delft University of Technology

Sebastiano Grazzi

The University of Warwick

Frank van der Meulen

Vrije Universiteit Amsterdam

Moritz Schauer

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Statistics and Computing

0960-3174 (ISSN) 1573-1375 (eISSN)

Vol. 33 8

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Control Engineering

DOI

10.1007/s11222-022-10180-5

More information

Latest update

1/4/2023 1