S. C. Kou, Qing Zhou, Wing H. Wong
Rejoinder to ``Equi-energy sampler with applications in statistical inference and statistical mechanics'' by Kou, Zhou and Wong [math.ST/0507080]
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Rejoinder: The ICML 2023 Ranking Experiment: Examining Author Self-Assessment in ML/AI Peer Review
本文回应了关于ICML 2023排名实验的讨论，将同行评审视为统计估计问题，探讨了等渗机制的公平性与策略问题，并提出了结合审稿人排名和生成式AI时代以人为中心的评审框架。
We introduce a new sampling algorithm, the equi-energy sampler, for efficient statistical sampling and estimation. Complementary to the widely used temperature-domain methods, the equi-energy sampler, utilizing the temperature--energy duality, targets the energy directly. The focus on the energy function not only facilitates efficient sampling, but also provides a powerful means for statistical estimation, for example, the calculation of the density of states and microcanonical averages in statistical mechanics. The equi-energy sampler is applied to a variety of problems, including exponential…
We present a Gibbs sampler for the Dempster-Shafer (DS) approach to statistical inference for Categorical distributions. The DS framework extends the Bayesian approach, allows in particular the use of partial prior information, and yields three-valued uncertainty assessments representing probabilities "for", "against", and "don't know" about formal assertions of interest. The proposed algorithm targets the distribution of a class of random convex polytopes which encapsulate the DS inference. The sampler relies on an equivalence between the iterative constraints of the vertex configuration and …
Discussion of ``EQUI-energy sampler'' by Kou, Zhou and Wong [math.ST/0507080]
Discussion of ``EQUI-energy sampler'' by Kou, Zhou and Wong [math.ST/0507080]
Markov chain Monte Carlo (MCMC) methods allow to sample a distribution known up to a multiplicative constant. Classical MCMC samplers are known to have very poor mixing properties when sampling multimodal distributions. The Equi-Energy sampler is an interacting MCMC sampler proposed by Kou, Zhou and Wong in 2006 to sample difficult multimodal distributions. This algorithm runs several chains at different temperatures in parallel, and allow lower-tempered chains to jump to a state from a higher-tempered chain having an energy 'close' to that of the current state. A major drawback of this algori…
We congratulate Samuel Kou, Qing Zhou and Wing Wong [math.ST/0507080] (referred to subsequently as KZW) for this beautifully written paper, which opens a new direction in Monte Carlo computation. This discussion has two parts. First, we describe a very closely related method, multicanonical sampling (MCS), and report a simulation example that compares the equi-energy (EE) sampler with MCS. Overall, we found the two algorithms to be of comparable efficiency for the simulation problem considered. In the second part, we develop some additional convergence results for the EE sampler.
An Exact Sampler for Inference after Polyhedral Model Selection
针对多面体刻画的模型选择事件，本文提出将约束变量变换到单位立方体的精确采样方法，支持单批样本多参数检验与置信区间构造，并实现选择调整似然的精确 MLE 计算。
In a recent paper `The equi-energy sampler with applications statistical inference and statistical mechanics' [Ann. Stat. 34 (2006) 1581--1619], Kou, Zhou & Wong have presented a new stochastic simulation method called the equi-energy (EE) sampler. This technique is designed to simulate from a probability measure $π$, perhaps only known up to a normalizing constant. The authors demonstrate that the sampler performs well in quite challenging problems but their convergence results (Theorem 2) appear incomplete. This was pointed out, in the discussion of the paper, by Atchadé & Liu (2006) who pro…
Novel sampling algorithms can significantly impact open questions in computational biology, most notably the in silico protein folding problem. By using computational methods, protein folding aims to find the three-dimensional structure of a protein chain given the sequence of its amino acid building blocks. The complexity of the problem strongly depends on the protein representation and its energy function. The more detailed the model, the more complex its corresponding energy function and the more challenge it sets for sampling algorithms. Kou, Zhou and Wong [math.ST/0507080] have introduced…
Comparing SGLD and a fixed-noise predictor-corrector adaptation in canonical joint energy-based models on CIFAR-10
本研究复现CIFAR-10上的规范联合能量基模型，发现预测-校正采样器与SGLD采样器无方法级优势差异，同时记录到两类失效模式。
Piecewise Deterministic Markov Processes for Bayesian Inference of PDE Coefficients
本文提出了一种基于分段确定性马尔可夫过程的框架，利用代理模型提升贝叶斯推断效率，特别适用于PDE系数的非线性反问题。
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