Selecting a subset of samples to label from a large pool of unlabeled data points, such that a sufficiently accurate classifier is obtained using a reasonably small training set is a challenging, yet critical problem. Challenging, since solving this problem includes cumbersome combinatorial computations, and critical, due to the fact that labeling is an expensive and time-consuming task, hence we always aim to minimize the number of required labels. While information theoretical objectives, such as mutual information (MI) between the labels
, have been successfully used in sequential querying, it is not straightforward to generalize these objectives to batch mode. This is because evaluation and optimization of functions which are trivial in individual querying settings become intractable for many objectives when we are to select multiple queries. In this paper, we develop a framework, where we propose efficient ways of evaluating and maximizing the MI between labels as an objective for batch mode active learning. Our proposed framework efficiently reduces the computational complexity from an order proportional to the batch size, when no approximation is applied, to the linear cost. The performance of this framework is evaluated using data sets from several fields showing that the proposed framework leads to efficient active learning for most of the data sets.
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