一种改进的相关向量回归方法

相关向量回归(relevance vector machine,RVR)是一种非线性回归方法。当样本集中存在少量异常点时,RVR方法能够得到鲁棒的回归模型。随着异常点增加,求得的回归模型的泛化能力下降。针对这种情况,实现了一种改进的相关向量回归方法。首先重新定义样本子集T和根据最小截平方和估计理论重新定义RVR回归的似然函数;然后利用贝叶斯推论求解边际最大似然函数;最后使用迭代法迭代求解最大似然函数的最优超参数α、β以及子集T,并使用超参数α、β得到回归模型。通过证明和实验结果表明,算法具有鲁棒性,而且当样本集中的异常点增加时,依然具有较高的鲁棒性。

An Improved Relevance Vector regression Method

Relevance vector regression (RVR) is a nonlinear regression method. When sample set has less abnormal points, the RVR could get the robust regression model. However, with the increasing of abnormal points, RVR becomes less effectiveness. In this paper, an advanced prediction model is developed to resolve this problem. First, the paper redefined subset T and likelihood function of the RVR based on least trimmed squares estimation. Then, it get the maximum marginal likelihood function by the way of Bayes' theorem. Finally , the iterative method was used to solve hyper parameters as well as subset T. Robust regression model was obtained with hyper parameters.The Proven and experimental results show that the method had more robustness . With the increasing of abnormal points, Regression performance was almost unchanged