Active learning (AL) concerns itself with learning a model from as few labelled data as possible through actively and iteratively querying an oracle with selected unlabelled samples. In this paper, we focus on analyzing a popular type of AL in which the utility of a sample is measured by a specified goal achieved by the retrained model after accounting for the samples marginal influence. Such AL strategies attract a lot of attention thanks to their intuitive motivations, yet they also suffer from impractically high computational costs due to their need for many iterations of model retraining. With the help of influence functions, we present an effective approximation that bypasses model retraining altogether, and propose a general efficient implementation that makes such AL strategies applicable in practice, both in the serial and the more challenging batch-mode setting. Additionally, we present both theoretical and empirical findings which call into question a few common practices and beliefs about such AL strategies.
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