energy-based sampling

While energy-parameterized diffusion models support Metropolis-Hastings (MH)-based MCMC sampling—yielding substantially improved sample quality under model composition—standard score-parameterized models lack an explicit energy function, preventing direct MH correction. Method: We propose Score-MCMC, a framework that reconstructs energy differences via line-integral approximations of the pre-trained score function, enabling derivation of a computable MH acceptance probability without modifying the underlying score model. Contribution/Results: Score-MCMC theoretically and practically bridges score-based and energy-based MCMC sampling. By coupling the diffusion reverse process with MH correction, it achieves sampling fidelity and diversity on par with energy-parameterized models across multiple benchmarks—particularly enhancing compositional distribution modeling in terms of both accuracy and sample diversity.

Traditional MCMC methods suffer from low sampling efficiency in complex distributions, while multi-proposal MCMC (MP-MCMC) offers parallelization potential but lacks a clear theoretical understanding of its behavior and optimization mechanisms under a large number of proposals. This work establishes a general theoretical framework for multi-proposal involutive MCMC in abstract state spaces, systematically analyzing the properties of transition kernels under various proposal and acceptance schemes. It introduces three novel algorithms (Algs. 1.1, 3.3, 3.4), unifies existing MP-MCMC approaches by revealing their intrinsic connections, and eliminates ineffective strategies. Through asymptotic analysis in the large-proposal limit and a unified modeling perspective, the study clarifies convergence and efficiency properties under high parallelism, providing both theoretical foundations and practical algorithms for large-scale parallel MCMC.

Bayesian inference under computationally expensive and nonsmooth likelihoods remains challenging due to prohibitive evaluation costs and the absence of reliable gradients. Method: This paper proposes a subset-driven delayed-acceptance MCMC framework comprising: (1) a data-driven surrogate model evaluated on random subsets—eliminating reliance on inaccurate gradients or Taylor approximations; (2) a computation-aware adaptive controller that jointly tunes proposal scale and subset size; and (3) a hierarchical delayed-acceptance mechanism that rapidly filters candidates via the coarse surrogate and rigorously validates them on the full dataset. Results: On real-world high-cost inference tasks—including disease modeling—the method significantly reduces sampling error under fixed computational budgets, balancing exploration efficiency and posterior accuracy. It outperforms state-of-the-art baselines (e.g., standard DA-MCMC, HINTS) in both convergence speed and estimation accuracy.

This study addresses the limitations of conventional subset simulation in accurately estimating failure probabilities when dealing with multiple failure regions, discontinuous, or highly nonlinear performance functions—challenges largely stemming from its reliance on the random-walk Metropolis sampler. To overcome these issues, this work proposes the first integration of the Intrepid MCMC sampler into the subset simulation framework, effectively mitigating sampling inefficiencies in multimodal, discontinuous, and high-dimensional failure domains. The proposed approach significantly enhances both the accuracy and robustness of failure probability estimation for complex reliability problems. Its superior performance is demonstrated across a range of benchmark examples spanning dimensions from 2 to 1003, confirming its effectiveness and scalability in practical applications.

To address the susceptibility of Markov chain Monte Carlo (MCMC) algorithms to local optima within the approximate Bayesian computation (ABC) framework, this paper proposes a global-local adaptive hybrid sampling scheme. The method iteratively constructs a dynamic global proposal distribution via importance resampling, while enhancing local move efficiency through Langevin dynamics integrated with common random numbers. It introduces, for the first time, a regularization-based normalizing flow approach to learn the importance sampling distribution, enabling adaptive optimization of its shape. Furthermore, an expected squared jump distance (ESJD)-driven adaptive coordination strategy is designed to balance exploration and exploitation. Experiments demonstrate substantial improvements in sampling efficiency and convergence reliability for complex multimodal posterior distributions. The implementation is publicly available on GitHub.

This study investigates the optimal scaling of high-dimensional Metropolised MCMC algorithms, focusing on how to adjust proposal distributions with increasing dimensionality to maintain sampling efficiency. Building upon the symmetry of the Metropolis–Hastings algorithm and high-dimensional asymptotic analysis, the authors develop a unified framework applicable to a broad class of target distributions and proposal mechanisms. The approach not only recovers classical results—such as the $O(1/d)$ variance scaling for Random Walk Metropolis (RWM) and $O(1/d^{1/3})$ for Metropolis-Adjusted Langevin Algorithm (MALA)—but also derives a novel class of gradient-driven MALA proposals with an optimal scaling law: their variance can be set to $O(1/d^\mu)$ for arbitrarily small $\mu > 0$, substantially outperforming existing methods. The theoretical analysis integrates non-product target measures and proposal distributions generated by implicit integrators of differential equations, demonstrating enhanced adaptability to dimensionality.

本文提出一种基于置信区域的筛选框架，用于解决模拟系统可接受性问题，保证高概率筛选出所有或每个可接受系统，并支持并行化。

This work addresses the challenge of inefficient posterior exploration in hierarchical discrete models with latent variables, where conventional MCMC methods struggle due to the need to integrate out latent variables. The authors propose a similarity-driven MCMC approach that constructs a proposal mechanism based on a data-driven measure of discrepancy between observations and model predictions, thereby guiding transitions toward regions of higher posterior support without explicitly integrating latent variables. This method represents the first application of similarity-driven proposals to discrete-space MCMC and is naturally suited to complex hierarchical discrete models. Experiments on both synthetic and real-world data demonstrate substantial improvements in sampling efficiency and posterior exploration, confirming its effectiveness in models such as Dirichlet–Multinomial regression.

本文提出Pref-MH方法，通过利用人类或模型裁判的成对比较来解决生成建模中条件采样问题，而无需直接评估目标密度。

本文研究了使用广义接受规则的Langevin提案的最佳缩放问题，针对高维目标提出了不同接受规则下的最优接受概率。