Word embedding-based similarity measures are currently among the top-performing methods on unsupervised semantic textual similarity (STS) tasks. Recent work has increasingly adopted a statistical view on these embeddings, with some of the top approaches being essentially various correlations (which include the famous cosine similarity). Another excellent candidate for a similarity measure is mutual information (MI), which can capture arbitrary dependencies between the variables and has a simple and intuitive expression. Unfortunately, its use in the context of dense word embeddings has so far been avoided due to difficulties with estimating MI for continuous data. In this work we go through a vast literature on estimating MI in such cases and single out the most promising methods, yielding a simple and elegant similarity measure for word embeddings. We show that mutual information is a viable alternative to correlations, gives an excellent signal that correlates well with human judgements of similarity and rivals existing state-of-the-art unsupervised methods.

Similarity measures based purely on word embeddings are comfortably competing with much more sophisticated deep learning and expert-engineered systems on unsupervised semantic textual similarity (STS) tasks. In contrast to commonly used geometric approaches, we treat a single word embedding as e.g. 300 observations from a scalar random variable. Using this paradigm, we first illustrate that similarities derived from elementary pooling operations and classic correlation coefficients yield excellent results on standard STS benchmarks, outperforming many recently proposed methods while being much faster and trivial to implement. Next, we demonstrate how to avoid pooling operations altogether and compare sets of word embeddings directly via correlation operators between reproducing kernel Hilbert spaces. Just like cosine similarity is used to compare individual word vectors, we introduce a novel application of the centered kernel alignment (CKA) as a natural generalisation of squared cosine similarity for sets of word vectors. Likewise, CKA is very easy to implement and enjoys very strong empirical results.

A large body of research into semantic textual similarity has focused on constructing state-of-the-art embeddings using sophisticated modelling, careful choice of learning signals and many clever tricks. By contrast, little attention has been devoted to similarity measures between these embeddings, with cosine similarity being used unquestionably in the majority of cases. In this work, we illustrate that for all common word vectors, cosine similarity is essentially equivalent to the Pearson correlation coefficient, which provides some justification for its use. We thoroughly characterise cases where Pearson correlation (and thus cosine similarity) is unfit as similarity measure. Importantly, we show that Pearson correlation is appropriate for some word vectors but not others. When it is not appropriate, we illustrate how common non-parametric rank correlation coefficients can be used instead to significantly improve performance. We support our analysis with a series of evaluations on word-level and sentence-level semantic textual similarity benchmarks. On the latter, we show that even the simplest averaged word vectors compared by rank correlation easily rival the strongest deep representations compared by cosine similarity.