Abstract-In this paper, a sparse learning algorithm, probabilistic classification vector machines (PCVMs), is proposed. We analyze relevance vector machines (RVMs) for classification problems and observe that adopting the same prior for different classes may lead to unstable solutions. In order to tackle this problem, a signed and truncated Gaussian prior is adopted over every weight in PCVMs, where the sign of prior is determined by the class label, i.e., +1 or 1. The truncated Gaussian prior not only restricts the sign of weights but also leads to a sparse estimation of weight vectors, and thus controls the complexity of the model. In PCVMs, the kernel parameters can be optimized simultaneously within the training algorithm. The performance of PCVMs is extensively evaluated on four synthetic data sets and 13 benchmark data sets using three performance metrics, error rate (ERR), area under the curve of receiver operating characteristic (AUC), and root mean squared error (RMSE). We compare PCVMs with soft-margin support vector machines (SVM Soft ), hard-margin support vector machines (SVM Hard ), SVM with the kernel parameters optimized by PCVMs (SVM PCVM ), relevance vector machines (RVMs), and some other baseline classifiers. Through five replications of twofold cross-validation test, i.e., 5 2 cross-validation test, over single data sets and Friedman test with the corresponding post-hoc test to compare these algorithms over multiple data sets, we notice that PCVMs outperform other algorithms, including SVM Soft , SVM Hard , RVM, and SVM PCVM , on most of the data sets under the three metrics, especially under AUC. Our results also reveal that the performance of SVM PCVM is slightly better than SVM Soft , implying that the parameter optimization algorithm in PCVMs is better than cross validation in terms of performance and computational complexity. In this paper, we also discuss the superiority of PCVMs' formulation using maximum a posteriori (MAP) analysis and margin analysis, which explain the empirical success of PCVMs.
Probabilistic classification vector machines (PCVMs) REF modify RVM by introducing a signed and truncated Gaussian prior over every weight, where the sign of the prior is determined by the class label.
Probabilistic Classification Vector Machines
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Computer Science Medicine