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Active Learning is a very common yet powerful framework for iteratively and adaptively sampling subsets of the unlabeled sets with a human in the loop with the goal of achieving labeling efficiency. Most real world datasets have imbalance either in classes and slices, and correspondingly, parts of the dataset are rare. As a result, there has been a lot of work in designing active learning approaches for mining these rare data instances. Most approaches assume access to a seed set of instances which contain these rare data instances. However, in the event of more extreme rareness, it is reasonable to assume that these rare data instances (either classes or slices) may not even be present in the seed labeled set, and a critical need for the active learning paradigm is to efficiently discover these rare data instances. In this work, we provide an active data discovery framework which can mine unknown data slices and classes efficiently using the submodular conditional gain and submodular conditional mutual information functions. We provide a general algorithmic framework which works in a number of scenarios including image classification and object detection and works with both rare classes and rare slices present in the unlabeled set. We show significant accuracy and labeling efficiency gains with our approach compared to existing state-of-the-art active learning approaches for actively discovering these rare classes and slices.