TY - JOUR
T1 - Sticky PDMP samplers for sparse and local inference problems
AU - Bierkens, Joris
AU - Grazzi, Sebastiano
AU - Meulen, Frank van der
AU - Schauer, Moritz
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - Bayesian variable selection
KW - Big-data
KW - High-dimensional problems
KW - Monte Carlo
KW - Non-reversible jump
KW - Piecewise deterministic Markov process
KW - Spike-and-slab
UR - http://www.scopus.com/inward/record.url?scp=85142909776&partnerID=8YFLogxK
U2 - 10.1007/s11222-022-10180-5
DO - 10.1007/s11222-022-10180-5
M3 - Article
AN - SCOPUS:85142909776
SN - 0960-3174
VL - 33
JO - Statistics and Computing
JF - Statistics and Computing
IS - 1
M1 - 8
ER -