  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.
