April Shen


pdf bib
Correlation Coefficients and Semantic Textual Similarity
Vitalii Zhelezniak | Aleksandar Savkov | April Shen | Nils Hammerla
Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers)

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.

pdf bib
Correlations between Word Vector Sets
Vitalii Zhelezniak | April Shen | Daniel Busbridge | Aleksandar Savkov | Nils Hammerla
Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)

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.