  The problem of learning to translate between two vector spaces given a set of
aligned points arises in several application areas of NLP. Current solutions
assume that the lexicon which defines the alignment pairs is noise-free. We
consider the case where the set of aligned points is allowed to contain an
amount of noise, in the form of incorrect lexicon pairs and show that this
arises in practice by analyzing the edited dictionaries after the cleaning
process. We demonstrate that such noise substantially degrades the accuracy of
the learned translation when using current methods. We propose a model that
accounts for noisy pairs. This is achieved by introducing a generative model
with a compatible iterative EM algorithm. The algorithm jointly learns the
noise level in the lexicon, finds the set of noisy pairs, and learns the
mapping between the spaces. We demonstrate the effectiveness of our proposed
algorithm on two alignment problems: bilingual word embedding translation, and
mapping between diachronic embedding spaces for recovering the semantic shifts
of words across time periods.
