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Active learning can actively select or construct examples to label to reduce the number of labeled examples needed for building accurate classifiers. However, previous works of active learning can only ask specific queries. For example, to predict osteoarthritis from a patient dataset with 30 attributes, specific queries always contain values of all these 30 attributes, many of which may be irrelevant. A more natural way is to ask "generalized queries" with don't-care attributes, such as "are people over 50 with knee pain likely to have osteoarthritis?" (with only two attributes: age and type of pain). We assume that the oracle (and human experts) can readily answer those generalized queries by returning probabilistic labels. The power of such generalized queries is that one generalized query may be equivalent to many specific ones. However, overly general queries may receive highly uncertain labels from the oracle, and this makes learning difficult. In this paper, we propose a novel active learning algorithm that asks generalized queries. We demonstrate experimentally that our new method asks significantly fewer queries compared with the previous works of active learning. Our method can be readily deployed in real-world tasks where obtaining labeled examples is costly.