Bayesian methods for support vector machines: Evidence and predictive class probabilities
Bayesian methods for support vector machines: Evidence and predictive class probabilities
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DOI：
10.1023/a:1012489924661
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发表时间：
2002-01-01
期刊：
影响因子：
7.5
通讯作者：
Sollich, P
中科院分区：
文献类型：
--
作者：
Sollich, P
我描述了一个框架，用于将支持向量机(SVMs)解释为具有高斯过程先验的推理问题的最大后验(MAP)解。这种概率解释可以为选择一个“好的”支持向量机核提供直观的指导。除此之外，它允许使用贝叶斯方法来解决支持向量机分类中的两个突出挑战：如何调整超参数-错误分类惩罚C和任何指定核的参数-以及如何获得预测性类别概率而不是传统的确定性类别标签预测。可以通过最大化证据来设置超参数；我将解释如何定义和适当地规范化后者。讨论了估计证据的解析近似方法和数值方法(蒙特卡罗链接)。我还比较了不同的估计类别概率的方法，从简单的地图评估或后验平均到后验完全平均。一个简单的玩具应用程序演示了各种概念和技术。
I describe a framework for interpreting Support Vector Machines (SVMs) as maximum a posteriori (MAP) solutions to inference problems with Gaussian Process priors. This probabilistic interpretation can provide intuitive guidelines for choosing a 'good' SVM kernel. Beyond this, it allows Bayesian methods to be used for tackling two of the outstanding challenges in SVM classification: how to tune hyperparameters-the misclassification penalty C, and any parameters specifying the ernel-and how to obtain predictive class probabilities rather than the conventional deterministic class label predictions. Hyperparameters can be set by maximizing the evidence; I explain how the latter can be defined and properly normalized. Both analytical approximations and numerical methods (Monte Carlo chaining) for estimating the evidence are discussed. I also compare different methods of estimating class probabilities, ranging from simple evaluation at the MAP or at the posterior average to full averaging over the posterior. A simple toy application illustrates the various concepts and techniques.