大數據時代的來臨，我們常面臨資料的標記品質不佳的情況。在傳統監督學習的二分類問題中，資料中含有部分的錯誤標記導致其訓練出的模型產生偏差。其中有一種含有錯誤標記的資料類型為僅含有正確標記的正標籤(positive)資料以及混雜大量負標籤(negative)及少量正標籤的未標記(unlabeled)資料，簡稱PU類型資料。在本文中我們比較文獻中所提出的三種邏輯斯迴歸的變型，分別是c-邏輯斯迴歸、ξ-邏輯斯迴歸以及γ-邏輯斯迴歸在PU類型資料的表現。我們藉由模擬實驗來比較這三種方法在PU類型資料下的參數估計準確性及分類正確性。實際資料分析使用UCI Machine Learning Repository中的兩筆資料集，分別是Wisconsin乳癌的資料集(WDBC)和Pima Indians糖尿病的資料集(Pima)。

With the advent of the big data era, we often face the situation of poor quality of labeling the data. In binary classification problems of traditional supervised learning, mislabeled in data leads to a model bias issues. One type of mislabeled data is which contains correctly labeled of positive data and unlabeled ones which mixed with a large number of negative data and a small number of positive data, referred to as positive and unlabeled data. In this article, we compare the three logistic regression variants proposed in the literature, namely c-logistic regression, ξ-logistic regression and γ-logistic regression on positive and unlabeled data. We compare the parameter estimation accuracies and classification correct rates of these three methods under positive and unlabeled data by simulation experiments. For real-world applications, we supply the three methods on the two datasets, WDBC (breast cancer Wisconsin (diagnostic)) data set and PIMA (Pima Indians diabetes) data set in the UCI Machine Learning Repository.

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