Główne pojęcia
Prior diffusion in Langevin algorithms enables dimension-independent convergence for non-log-concave distributions.
Streszczenie
Abstract:
Dimension dependency in high-dimensional sampling is crucial.
Biased samplers like Underdamped Langevin Dynamics perform better in low-accuracy cases.
Introduction:
Sampling from unnormalized distributions is fundamental.
Langevin algorithms leverage the Stein score for practicality.
Related Work:
Biased samplers have dimension dependency.
Unbiased samplers have iteration complexity related to log(1/ϵ).
Problem Setup:
Sampling from posterior distributions aims to obtain particles.
Notations and problem settings are introduced.
Theoretical Results:
Convergence rates of Langevin algorithms with prior diffusion are discussed.
Discussion:
LAPD offers dimension-independent convergence.
Specific examples and Gaussian mixtures are discussed.
Conclusions and Future Work:
Future research directions are proposed.
Statystyki
Freund et al. (2022) suggests dimension-independent convergence rate for Langevin algorithms.
LAPD convergence rate is dimension-independent.
Cytaty
"The convergence rate of LAPD only depends on the number of mixture components K and the radius of means Rµ." - Huang et al. (2024b)