A fast algorithm for multi-class learning from label proportions

Learning from label proportions (LLP) is a new kind of learning problem which has attracted wide interest in machine learning. Different from the well-known supervised learning, the training data of LLP is in the form of bags and only the proportion of each class in each bag is available. Actually, many modern applications can be successfully abstracted to this problem such as modeling voting behaviors and spam filtering. However, time-consuming training is still a challenge for LLP, which becomes a bottleneck especially when addressing large bags and bag sizes. In this paper, we propose a fast algorithm called multi-class learning from label proportions by extreme learning machine (LLP-ELM), which takes advantage of an extreme learning machine with fast learning speed to solve multi-class learning from label proportions. Firstly, we reshape the hidden layer output matrix and the training data target matrix of an extreme learning machine to adapt to the proportion information instead of the real labels. Secondly, a robust loss function with a regularization term is formulated and two efficient solutions are provided to different cases. Finally, various experiments demonstrate the significant speed-up of the proposed model with better accuracies on different datasets compared with several state-of-the-art methods.