As supervised fine-tuning of pre-trained models within NLP applications increases in popularity, larger corpora of annotated data are required, especially with increasing parameter counts in large language models. Active learning, which attempts to mine and annotate unlabeled instances to improve model performance maximally fast, is a common choice for reducing the annotation cost; however, most methods typically ignore class imbalance and either assume access to initial annotated data or require multiple rounds of active learning selection before improving rare classes. We present STENCIL, which utilizes a set of text exemplars and the recently proposed submodular mutual information to select a set of weakly labeled rare-class instances that are then strongly labeled by an annotator. We show that STENCIL improves overall accuracy by $10\%-24\%$ and rare-class F-1 score by $17\%-40\%$ on multiple text classification datasets over common active learning methods within the class-imbalanced cold-start setting.

Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a set of random variables is submodular. In this paper, we study combinatorial information measures that generalize independence, (conditional) entropy, (conditional) mutual information, and total correlation defined over sets of (not necessarily random) variables. These measures strictly generalize the corresponding entropic measures since they are all parameterized via submodular functions that themselves strictly generalize entropy. Critically, we show that, unlike entropic mutual information in general, the submodular mutual information is actually submodular in one argument, holding the other fixed, for a large class of submodular functions whose third-order partial derivatives satisfy a non-negativity property. This turns out to include a number of practically useful cases such as the facility location and set-cover functions. We study specific instantiations of the submodular information measures on these, as well as the probabilistic coverage, graph-cut, and saturated coverage functions, and see that they all have mathematically intuitive and practically useful expressions. Regarding applications, we connect the maximization of submodular (conditional) mutual information to problems such as mutual-information-based, query-based, and privacy-preserving summarization -- and we connect optimizing the multi-set submodular mutual information to clustering and robust partitioning.