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Despite the recent successes of deep learning in natural language processing(NLP), there remains widespread usage of and demand for techniques that do notrely on machine learning. The advantage of these techniques is theirinterpretability and low cost when compared to frequently opaque and expensivemachine learning models. Although they may not be be as performant in allcases, they are often sufficient for common and relatively simple problems. Inthis paper, we aim to modernize these older methods while retaining theiradvantages by extending approaches from categorical or bag-of-wordsrepresentations to word embeddings representations in the latent space. First,we show that entropy and Kullback-Leibler divergence can be efficientlyestimated using word embeddings and use this estimation to compare text acrossseveral categories. Next, we recast the heavy-tailed distribution known asZipf's law that is frequently observed in the categorical space to the latentspace. Finally, we look to improve the Jaccard similarity measure for sentencesuggestion by introducing a new method of identifying similar sentences basedon the set cover problem. We compare the performance of this algorithm againstseveral baselines including Word Mover's Distance and the Levenshtein distance.

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