多重跳跃MCMC：用于二元模型空间贝叶斯推断的可扩展算法
Multiple Jump MCMC: A Scalable Algorithm for Bayesian Inference on Binary Model Spaces
AI总结：
本文提出多重跳跃MCMC算法，用于二元模型空间的贝叶斯推断，该算法简单、无拒绝机制且速度快，适用于高斯图模型、异或模型和变量选择等场景。
摘要：
本文考虑了二元模型空间的贝叶斯模型推断。二元模型空间被广泛应用于图模型、变量选择、混合分布和决策树等模型中。传统方法如可逆跳跃或生灭MCMC算法尽管仍流行，但存在探索模型空间缓慢的问题。本文提出了一种替代方法：多重跳跃MCMC算法。该算法简单、无拒绝机制且速度显著。当应用于无向高斯图模型时，其速度比现有最佳方法快100到200倍，可在一分钟内解决具有500,000个参数的模型。我们提供了定理，说明我们的算法如何准确地瞄准后验分布，并展示了如何将我们的框架应用于高斯图模型、异或模型和变量选择，但指出它适用于大多数二元模型空间的贝叶斯后验推断。
英文摘要：
This article considers Bayesian model inference on binary model spaces. Binary model spaces are used by a large class of models, including graphical models, variable selection, mixture distributions, and decision trees. Traditional strategies in this field, such as reversible jump or birth-death MCMC algorithms, are still popular, despite suffering from a slow exploration of the model space. In this article, we propose an alternative: the Multiple Jump MCMC algorithm. The algorithm is simple, rejection-free, and remarkably fast. When applied to undirected Gaussian graphical models, it is 100 to 200 times faster than the state-of-the-art, solving models with $500,000$ parameters in less than a minute. We provide theorems showing how accurately our algorithm targets the posterior, and we show how to apply our framework to Gaussian graphical models, Ising models, and variable selection, but note that it applies to most Bayesian posterior inference on binary model spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
