Importance weighted passive learning

Importance weighted active learning (IWAL) introduces a weighting scheme to measure the importance of each instance for correcting the sampling bias of the probability distributions between training and test datasets. However, the weighting scheme of IWAL involves the distribution of the test data, which can be straightforwardly estimated in active learning by interactively querying users for labels of selected test instances, but difficult for conventional learning where there are no interactions with users, referred as passive learning. In this paper, we investigate the insufficient sampling bias problem, i.e., bias occurs only because of insufficient samples, but the sampling process is unbiased. In doing this, we present two assumptions on the sampling bias, based on which we propose a practical weighting scheme for the empirical loss function in conventional passive learning, and present IWPL, an importance weighted passive learning framework. Furthermore, we provide IWSVM, an importance weighted SVM for validation. Extensive experiments demonstrate significant advantages of IWSVM on benchmarks and synthetic datasets.