BLISS in Non-Isometric Embedding Spaces
Authors: Barun Patra, Joel Ruben Antony Moniz, Sarthak Garg, Matthew R Gormley, Graham Neubig
Keywords: bilingual lexicon induction, semi-supervised methods, embeddings
TL;DR: A novel method to test for isometry between word embedding spaces, and a semi-supervised method for learning better mappings between them
Abstract: Recent work on bilingual lexicon induction (BLI) has frequently depended either on aligned bilingual lexicons or on distribution matching, often with an assumption about the isometry of the two spaces. We propose a technique to quantitatively estimate this assumption of the isometry between two embedding spaces and  empirically show that this assumption weakens as the languages in question become increasingly etymologically distant. We then propose Bilingual Lexicon Induction with Semi-Supervision (BLISS) --- a novel semi-supervised approach that relaxes the isometric assumption while leveraging both limited aligned bilingual lexicons and a larger set of unaligned word embeddings, as well as a novel hubness filtering technique. Our proposed method improves over strong baselines for 11 of 14 on the MUSE dataset, particularly for languages whose embedding spaces do not appear to be isometric. In addition, we also show that adding supervision stabilizes the learning procedure, and is effective even with minimal supervision.