Correlation Coefficients and Semantic Textual Similarity
This work addresses the overlooked issue of similarity measures in NLP for researchers and practitioners, offering a simple yet effective improvement over standard methods, though it is incremental in nature.
The paper tackled the problem of semantic textual similarity by showing that cosine similarity is often equivalent to Pearson correlation for word vectors, but is unfit in some cases, and demonstrated that using rank correlation coefficients instead can significantly improve performance, with simple averaged word vectors rivaling deep representations on benchmarks.
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.