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 three real life datasets.

翻译：热量矢量机(RVM)是一种流行的稀有贝叶西亚学习模型,通常用于预测。最近,已经表明,在RVM的多重处罚参数上假设不适当的前科假设可能导致不适当的后遗症。目前在文献中,对于RVM的后遗症而言,充分的后遗症条件不允许对多重处罚参数作不适当的前科。在本篇文章中,我们提出了一个单一的惩罚相关矢量机(SPRVM)模型,其中多重处罚参数被单一刑罚取代,我们考虑采用半巴伊西亚方法来配合SPRVM。SPRVM的后遗症性能必要和充分的条件比RVM更为宽松,并允许在处罚参数上出现若干不适当的前科。此外,我们还证明Gibs取样器用于分析SPRVM模型的几何测量性能,因此可以估计与蒙卡洛对后遗症预测分布式分布式分布法有关的标准错误。在RVM的情况下,无法计算出SPRV的后遗症标准错误,因为GIFS的预测结果的实际趋同率是RM使用的S的比M。