This paper presents a latent variable representation of regularized support vector machines (SVM's) that enables EM, ECME or MCMC algorithms to provide parameter estimates. We verify our representation by demonstrating that minimizing the SVM optimality criterion together with the parameter regularization penalty is equivalent to finding the mode of a mean-variance mixture of normals pseudo-posterior distribution. The latent variables in the mixture representation lead to EM and ECME point estimates of SVM parameters, as well as MCMC algorithms based on Gibbs sampling that can bring Bayesian tools for Gaussian linear models to bear on SVM's. We show how to implement SVM's with spike-and-slab priors and run them against data from a standard spam filtering data set.

Nicholas G. Polson

Steven L. Scott

Bayesian Analysis

贝叶斯分析是国际贝叶斯分析学会的电子期刊。它旨在发表广泛的文章，在某些理论或应用背景下展示或讨论贝叶斯方法。该期刊欢迎提交新的计算和统计方法的投稿；对现有方法的批判性审查和讨论；历史观点；重要科学或政策应用领域的描述；实例探究;以及实验设计、数据收集、数据共享或数据挖掘的方法。提交的评估基于内容的重要性和沟通的有效性。讨论论文通常由主编选择，或由编辑建议，在定期提交的论文中。此外，《期刊》鼓励个人作者提交手稿以作为讨论文件考虑。

Bayesian Analysis is the electronic journal of the International Society for Bayesian Analysis. It aims to publish a wide range of articles that showcase or discuss Bayesian methods in various theoretical or applied contexts. The journal welcomes submissions of new computational and statistical methods; critical reviews and discussions of existing methods; historical perspectives; descriptions of significant scientific or policy application areas; case studies; as well as methods for experimental design, data collection, data sharing, or data mining. Submitted papers are evaluated based on the importance of their content and the effectiveness of their communication. Discussion papers are typically selected by the editor-in-chief or recommended by editors as part of regularly submitted papers. Additionally, Bayesian Analysis encourages individual authors to submit manuscripts for consideration as discussion papers.

《Bayesian Analysis》是国际贝叶斯分析学会的电子期刊，旨在发表广泛的文章，展示或讨论贝叶斯方法在各种理论或应用背景下的应用。该期刊欢迎提交新的计算和统计方法的研究；对现有方法的批判性审查和讨论；历史视角；重要科学或政策应用领域的描述；实例研究；以及实验设计、数据收集、数据共享或数据挖掘的方法。提交的论文将根据内容的重要性和沟通的有效性进行评估。讨论论文通常由主编选择，或由编辑建议，作为定期提交的论文的一部分。此外，《Bayesian Analysis》鼓励个人作者提交手稿，以供作为讨论文件考虑。

Data augmentation for support vector machines

A latent variable representation of regularized support vector machines that enables EM, ECME or MCMC algorithms to provide parameter estimates and shows how to implementing SVM’s with spike-and-slab priors and running them against data from a standard spam filtering data set.

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数学, 统计学与概率论	2

Data augmentation for support vector machines

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