On Extending NLP Techniques from the Categorical to the Latent Space: KL Divergence, Zipf's Law, and Similarity Search

Despite the recent successes of deep learning in natural language processing (NLP), there remains widespread usage of and demand for techniques that do not rely on machine learning. The advantage of these techniques is their interpretability and low cost when compared to frequently opaque and expensive machine learning models. Although they may not be be as performant in all cases, they are often sufficient for common and relatively simple problems. In this paper, we aim to modernize these older methods while retaining their advantages by extending approaches from categorical or bag-of-words representations to word embeddings representations in the latent space. First, we show that entropy and Kullback-Leibler divergence can be efficiently estimated using word embeddings and use this estimation to compare text across several categories. Next, we recast the heavy-tailed distribution known as Zipf's law that is frequently observed in the categorical space to the latent space. Finally, we look to improve the Jaccard similarity measure for sentence suggestion by introducing a new method of identifying similar sentences based on the set cover problem. We compare the performance of this algorithm against several baselines including Word Mover's Distance and the Levenshtein distance.