  Cross-lingual transfer of word embeddings aims to establish the semantic
mappings among words in different languages by learning the transformation
functions over the corresponding word embedding spaces. Successfully solving
this problem would benefit many downstream tasks such as to translate text
classification models from resource-rich languages (e.g. English) to
low-resource languages. Supervised methods for this problem rely on the
availability of cross-lingual supervision, either using parallel corpora or
bilingual lexicons as the labeled data for training, which may not be available
for many low resource languages. This paper proposes an unsupervised learning
approach that does not require any cross-lingual labeled data. Given two
monolingual word embedding spaces for any language pair, our algorithm
optimizes the transformation functions in both directions simultaneously based
on distributional matching as well as minimizing the back-translation losses.
We use a neural network implementation to calculate the Sinkhorn distance, a
well-defined distributional similarity measure, and optimize our objective
through back-propagation. Our evaluation on benchmark datasets for bilingual
lexicon induction and cross-lingual word similarity prediction shows stronger
or competitive performance of the proposed method compared to other
state-of-the-art supervised and unsupervised baseline methods over many
language pairs.
