Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusion

Основні поняття

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.

Анотація

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)))

Цитати

"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."

Ключові висновки, отримані з

Zeroth-Order Sampling Methods for Non-Log-Concave Distributions

by Ye He,Kevin ... о arxiv.org 02-29-2024

https://arxiv.org/pdf/2402.17886.pdf

Глибші Запити

How does ZOD-MC compare to other sampling algorithms in terms of computational efficiency

ZOD-MC demonstrates superior computational efficiency compared to other sampling algorithms in various ways. Firstly, ZOD-MC leverages zeroth-order queries, which are less computationally intensive than first-order queries used in traditional sampling algorithms. This reduction in computational complexity allows ZOD-MC to achieve high accuracy with fewer function evaluations, making it more efficient in terms of resource utilization.
Moreover, ZOD-MC's rejection sampling approach enables it to sample from non-logconcave distributions efficiently by constructing an envelope for the target distribution. This method eliminates the need for complex gradient computations and expensive acceptance-rejection steps commonly found in other algorithms. By optimizing the rejection process and utilizing a mix of KL divergence and Wasserstein-2 distance criteria, ZOD-MC can generate accurate samples with minimal computational overhead.
In practical applications where computational resources are limited or time constraints exist, ZOD-MC's computational efficiency makes it a valuable tool for sampling from challenging distributions effectively.

What are the implications of using zeroth-order queries instead of first-order queries in sampling algorithms

Using zeroth-order queries instead of first-order queries in sampling algorithms has significant implications on both theoretical analysis and practical implementation:

Reduced Computational Complexity: Zeroth-order queries only require access to function values without needing gradients or higher derivatives. This simplification leads to lower computation costs since evaluating functions is typically faster and less resource-intensive than computing gradients.

Broader Applicability: First-order methods often rely on smoothness assumptions about the target distribution or potential function. In contrast, zeroth-order methods like ZOD-MC can handle non-smooth or discontinuous potentials without compromising performance. This broader applicability allows for more versatile use cases across different domains.

Ease of Implementation: Implementing zeroth-order query-based algorithms is generally simpler as they do not involve calculating gradients or dealing with derivative-related challenges such as vanishing/exploding gradients. This simplicity facilitates quicker development cycles and easier integration into existing systems.

Insensitivity to Gradient Accuracy: Zeroth-order methods like ZOD-MC are robust against inaccuracies in gradient estimates that may arise from noise or approximation errors during computation.

How can ZOD-MC's insensitivity to mode separation be leveraged in practical applications beyond statistical inference

ZOD-MC's insensitivity to mode separation offers several advantages that can be leveraged in practical applications beyond statistical inference:

Robust Sampling:

In scenarios where modes are widely separated or exhibit complex geometries, such as multimodal distributions with distant peaks, ZOD-MC's ability to sample accurately across all modes ensures robust exploration of the entire distribution space.

2 .Metastability Mitigation:

Applications involving metastable states benefit from ZOD-MCs' capability to navigate high-energy barriers between modes efficiently.
3 .Anomaly Detection:
- Leveraging this insensitivity could enhance anomaly detection systems by enabling effective identification of rare events even when surrounded by dominant data clusters.
4 .Generative Modeling
- In generative modeling tasks like image generation where capturing diverse patterns is crucial,ZOCDMC’s resilience towards mode separation aids in producing realistic samples encompassing various features present within the dataset.
Overall,ZOCDMC’s adaptability towards varying degrees of mode separation enhances its utility across diverse fields requiring reliable probabilistic modeling capabilities..