有序多分类方法已经得到了广泛研究。传统的有序多分类方法假设样本的类别标签是不存在误标记的。但是由于实际数据复杂以及人工经验有限,获得标记完全正确的样本是不现实的,因此,传统的方法就存在局限性。提出一种基于γ-散度的有序误标记logistic回归方法,在处理存在误标记的有序多分类问题时具有很强的稳健性,也就是说,当某一样本被错误标记时它对参数估计的权重小于其被正确标记时的权重。该方法通过最小化γ-散度构建模型,利用梯度下降算法求解模型,不仅具有很强的稳健性而且在模型中可以忽略误标记概率。模拟研究和真实数据分析都说明该有序误标记logistic回归方法在处理存在误标记的有序分类问题时效果很好。
Ordinal multi-classification methods have been studied widely. Traditional ordinal multi-classification methods assume that the sample label is not mislabeled. Due to the complexity of the real data and the limited artificial experience, it is unrealistic to obtain completely accurate labels, in which conventional methods perform poorly. In this article, we propose an ordinal mislabel logistic regression method based on γ-divergence, which possessing strong robustness when dealing with ordinal mislabeled response data. That is to say, when mislabeled, the weight of the sample in parameter estimation equation diminish compared to the case that the sample is properly labeled. Our method not only possesses the robustness but also can ignore the mislabel probabilities in the model. We construct the model by minimizing γ-divergence estimation and solve the model by gradient descent algorithm. Both simulation studies and real data analysis demonstrate that the method, namely robust ordinal mislabel logistic regression, is efficient to analyze ordinal mislabeled response data.
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