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关注这篇论文的作者
Veronika Ročková

用于变量选择的粒子 EM 算法

研究问题
尖峰厚尾先验下的贝叶斯变量选择后验具有多个局部峰值时,如何减少 EM 的局部陷阱,并概括模型选择不确定性?
方法与思路
作者提出由相互排斥粒子组成的群体 EM 搜索,同时给出探索退火后验序列的序贯蒙特卡洛变体,以捕捉多个模式。
材料陈述的贡献
摘要称,粒子 EM 可通过重要模式及其权重确定性重构后验以近似贝叶斯推断,渐近分析提示稀疏情形不必使用大量粒子。
阅读关注点
应核对粒子相互作用、模式权重与后验重构的计算方式,以及粒子数结论的条件和对遗漏模式的敏感性。
阅读边界
依据版本未注明的 OpenAlex 索引摘要;摘要未提供全局最优保证、近似误差界或实际粒子数,不能将模式重构视为精确后验或推断刊本变化。

原文摘要

Despite its long history of success, the EM algorithm has been vulnerable to local entrapment when the posterior/likelihood is multi-modal. This is particularly pronounced in spike-and-slab posterior distributions for Bayesian variable selection. The main thrust of this article is to introduce the particle EM algorithm, a new population-based optimization strategy that harvests multiple modes in search spaces that present many local maxima. Motivated by nonparametric variational Bayes strategies, particle EM achieves this goal by deploying an ensemble of interactive repulsive particles. These particles are geared toward uncharted areas of the posterior, providing a more comprehensive summary of its topography than simple parallel EM deployments. A sequential Monte Carlo variant of particle EM is also proposed that explores a sequence of annealed posteriors by sampling from a set of mutually avoiding particles. Particle EM outputs a deterministic reconstruction of the posterior distribution for approximate fully Bayes inference by capturing its essential modes and mode weights. This reconstruction reflects model selection uncertainty and is supported by asymptotic considerations, which indicate that the requisite number of particles need not be large in the presence of sparsity (when p > n). Supplementary materials for this article are available online.

笔记与分组
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