Relevance vector machine (RVM) is a popular sparse Bayesian learning model typically used for prediction. Recently it has been shown that improper priors assumed on multiple penalty parameters in RVM may lead to an improper posterior. Currently in the literature, the sufficient conditions for posterior propriety of RVM do not allow improper priors over the multiple penalty parameters. In this article, we propose a single penalty relevance vector machine (SPRVM) model in which multiple penalty parameters are replaced by a single penalty and we consider a semi-Bayesian approach for fitting the SPRVM. The necessary and sufficient conditions for posterior propriety of SPRVM are more liberal than those of RVM and allow for several improper priors over the penalty parameter. Additionally, we also prove the geometric ergodicity of the Gibbs sampler used to analyze the SPRVM model and hence can estimate the asymptotic standard errors associated with the Monte Carlo estimate of the means of the posterior predictive distribution. Such a Monte Carlo standard error cannot be computed in the case of RVM, since the rate of convergence of the Gibbs sampler used to analyze RVM is not known. The predictive performance of RVM and SPRVM is compared by analyzing two simulation examples and three real life datasets.

中文翻译：

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使用单一惩罚方法分析相关向量机

相关向量机 (RVM) 是一种流行的稀疏贝叶斯学习模型，通常用于预测。最近已经表明，在 RVM 中对多个惩罚参数假设的不正确的先验可能会导致不正确的后验。目前在文献中，RVM 后验适当性的充分条件不允许对多个惩罚参数进行不适当的先验。在本文中，我们提出了一个单惩罚相关向量机 (SPRVM) 模型，其中多个惩罚参数被一个惩罚替换，我们考虑了一种半贝叶斯方法来拟合 SPRVM。SPRVM 的后验适当性的充分必要条件比 RVM 更自由，并且允许在惩罚参数上存在多个不适当的先验。此外，我们还证明了用于分析 SPRVM 模型的 Gibbs 采样器的几何遍历性，因此可以估计与后验预测分布均值的 Monte Carlo 估计相关的渐近标准误差。这种蒙特卡罗标准误差在 RVM 的情况下无法计算，因为用于分析 RVM 的 Gibbs 采样器的收敛速度是未知的。通过分析两个仿真示例和三个现实生活数据集，比较了 RVM 和 SPRVM 的预测性能。