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Sticky PDMP samplers for sparse and local inference problems
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Bierkens, Joris, Grazzi, Sebastiano, Meulen, Frank van der and Schauer, Moritz (2023) Sticky PDMP samplers for sparse and local inference problems. Statistics and Computing, 33 (1). 8. doi:10.1007/s11222-022-10180-5 ISSN 0960-3174.
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Official URL: https://doi.org/10.1007/s11222-022-10180-5
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.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
SWORD Depositor: | Library Publications Router | ||||||||
Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory, Mathematical statistics, Markov processes, Big Data -- Distributed processing | ||||||||
Journal or Publication Title: | Statistics and Computing | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0960-3174 | ||||||||
Official Date: | 2023 | ||||||||
Dates: |
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Volume: | 33 | ||||||||
Number: | 1 | ||||||||
Number of Pages: | 31 | ||||||||
Article Number: | 8 | ||||||||
DOI: | 10.1007/s11222-022-10180-5 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 4 January 2023 | ||||||||
Date of first compliant Open Access: | 5 January 2023 | ||||||||
RIOXX Funder/Project Grant: |
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