Game-theoretic Vocabulary Selection via the Shapley Value and Banzhaf Index

The input vocabulary and the representations learned are crucial to the performance of neural NLP models. Using the full vocabulary results in less explainable and more memory intensive models, with the embedding layer often constituting the majority of model parameters. It is thus common to use a smaller vocabulary to lower memory requirements and construct more interpertable models. We propose a vocabulary selection method that views words as members of a team trying to maximize the model’s performance. We apply power indices from cooperative game theory, including the Shapley value and Banzhaf index, that measure the relative importance of individual team members in accomplishing a joint task. We approximately compute these indices to identify the most influential words. Our empirical evaluation examines multiple NLP tasks, including sentence and document classification, question answering and textual entailment. We compare to baselines that select words based on frequency, TF-IDF and regression coefficients under L1 regularization, and show that this game-theoretic vocabulary selection outperforms all baseline on a range of different tasks and datasets.