English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Langevin diffusion (LD) is one of the main workhorses for sampling problems.However, its convergence rate can be significantly reduced if the targetdistribution is a mixture of multiple densities, especially when each componentconcentrates around a different mode. Replica exchange Langevin diffusion(ReLD) is a sampling method that can circumvent this issue. In particular, ReLDadds another LD sampling a high-temperature version of the target density, andexchange the locations of two LDs according to a Metropolis-Hasting type oflaw. This approach can be further extended to multiple replica exchangeLangevin diffusion (mReLD), where $K$ additional LDs are added to sampledistributions at different temperatures and exchanges take place betweenneighboring-temperature processes. While ReLD and mReLD have been usedextensively in statistical physics, molecular dynamics, and other applications,there is little existing analysis on its convergence rate and choices oftemperatures. This paper closes these gaps assuming the target distribution isa mixture of log-concave densities. We show ReLD can obtain constant or evenbetter convergence rates even when the density components of the mixtureconcentrate around isolated modes. We also show using mReLD with $K$ additionalLDs can achieve the same result while the exchange frequency only needs to be$(1/K)$-th power of the one in ReLD.

Spectral Gap of Replica Exchange Langevin Diffusion on Mixture Distributions