Основные понятия
This paper introduces Zeroth-Order Diffusion Monte Carlo (ZOD-MC) as an efficient sampler for non-log-concave distributions, addressing metastability issues through denoising diffusion. The approach leverages zeroth-order queries without isoperimetric assumptions, showcasing superior performance in low-dimensional settings.
Аннотация
Zeroth-Order Sampling Methods for Non-Log-Concave Distributions explores the development of ZOD-MC, a novel algorithm that efficiently samples from challenging distributions without requiring isoperimetric conditions. By leveraging denoising diffusion and rejection sampling, ZOD-MC demonstrates insensitivity to mode separation and discontinuities in potential functions. The method outperforms existing samplers like RDMC and RS-DMC, offering promising results in various scenarios.
The paper discusses the theoretical foundations of ZOD-MC, including convergence analyses and complexity bounds. It highlights the advantages of zeroth-order queries over first-order methods, emphasizing computational efficiency and accuracy in sampling tasks. Experimental results showcase ZOD-MC's robustness in handling asymmetric Gaussian mixtures, mode separation challenges, and discontinuous potentials like the M¨uller Brown potential.
Статистика
O(dε−1)
exp(O(log(d)) ˜O(ε−1))
exp(O(log3(dε−1)))
O(dε−1)
exp( ˜O(d)O(log(ε−1)))
Цитаты
"The advantages of our algorithm are experimentally verified for non-log-concave target distributions."
"ZOD-MC excels in low-dimensions without isoperimetric assumptions."
"Our result provides theoretical insight on optimal step-size choices."