Transfer Learning-Based Label Proportions Method with Data of Uncertainty

Learning with label proportions(LLP), which seeks an instance-level classifier merely based on bag-level label proportions, is a new paradigm in machine learning that addresses the classification of instances [1, 2, 3]. In LLP, we only know the proportions of examples belonging to different classes in each bag; however the labels of the instances are unknown. From the binary classification perspective, the task of LLP is to learn a classifier to classify the unknown label instance as either positive class or negative class. The formulation that learning with label proportions has been first proposed by Kuck et al. in [1], which can be used for political elections analysis. In the case of politician polls, each candidate may have a group of loyal voters and some swing voters. They may know the vague proportion of votes cast in each district; however, they usually do not know the vote of each person. Since the candidates have limited resources, they have to analyze political elections and consider which kind of voters they should focus on so as to maximize their interests. To date, LLP has been applied to forecasting revenue [4], image classification [5, 6], video event detection [7], demographics mining [8] and privacy protection [9]. Figure 1 illustrates the binary classification problem in LLP.