We develop a new sampling strategy that uses the hit-and-run algorithm within level sets of the target density. Our method can be applied to any quasi-concave density, which covers a broad class of models. Our sampler performs well in high-dimensional settings, which we illustrate with a comparison to Gibbs sampling on a spike-and-slab mixture model. We also extend our method to exponentially-tilted quasi-concave densities, which arise often in Bayesian models consisting of a log-concave likelihood and quasi-concave prior density. Within this class of models, our method is effective at sampling from posterior distributions with high dependence between parameters, which we illustrate with a simple multivariate normal example. We also implement our level-set sampler on a Cauchy-normal model where we demonstrate the ability of our level set sampler to handle multi-modal posterior distributions.
Constrained and Composite Sampling via Proximal Sampler
Department of Computer Science, University of Rochester（计算机科学系，罗切斯特大学）；Goergen Institute for Data Science and Artificial Intelligence (GIDS-AI)（数据科学与人工智能研究所（GIDS-AI））
On the Computational Efficiency of Bayesian Additive Regression Trees: An Asymptotic Analysis
Department of Statistics and Data Science, National University of Singapore（统计与数据科学系，新加坡国立大学）；Department of Statistics, UC Berkeley（统计系，加州大学伯克利分校）；Department of Electrical Engineering and Computer Sciences, UC Berkeley（电气工程与计算机科学系，加州大学伯克利分校）；Center for Computational Biology, UC Berkeley（计算生物学中心，加州大学伯克利分校）
Non-reversible, tuning- and rejection-free Markov chain Monte Carlo via iterated random functions
在这项工作中，我们提出了一个不可逆的，调整和拒绝免费的马尔可夫链蒙特卡罗，自然适合在打了就跑的框架。采样器只需要访问对数密度函数的梯度，因此不需要归一化常数。我们证明了所提出的马尔可夫链是不变的目标分布，并说明其适用性，通过广泛的例子。我们表明，本文中介绍的采样器与Peters and de With（2012），Bouchard-Cote et al.（2017）的连续采样器密切相关。特别是，计算是非常相似的，在这个意义上，都是围绕模拟一个非均匀泊松过程。当对数密度的梯度允许将计算有效的方向分解为两个单调函数之和时，计算可以被简化。我们将我们的采样器应用于选择性推理，比以前使用的采样器有了显著的改进（Tian et al. 2016）。
Scalable Logistic Gaussian Process Density Regression with Kinetic Langevin Sampling
Nanyang Technological University（南洋理工大学）；Eötvös Loránd University (ELTE)（厄特沃什·罗兰大学（ELTE））；HUN-REN Institute for Computer Science and Control (SZTAKI)（匈牙利国家研究网络计算机科学与控制研究所（SZTAKI））
Faster Sampling without Isoperimetry via Diffusion-based Monte Carlo
Hong Kong University of Science and Technology（香港科技大学）；The University of Hong Kong（香港大学）；University of California San Diego（加利福尼亚大学圣迭戈分校）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
本文针对 Diffusion-based Monte Carlo 梯度复杂度过高的问题，提出基于递归得分估计的 RS-DMC 算法，通过片段分解使采样子问题只需处理强对数凹分布，将梯度复杂度从指数级降为拟多项式级，并证明在耗散条件下优于 Langevin 类算法。
