  Cross-lingual word embeddings aim to capture common linguistic regularities
of different languages, which benefit various downstream tasks ranging from
machine translation to transfer learning. Recently, it has been shown that
these embeddings can be effectively learned by aligning two disjoint
monolingual vector spaces through a linear transformation (word mapping). In
this work, we focus on learning such a word mapping without any supervision
signal. Most previous work of this task adopts parametric metrics to measure
distribution differences, which typically requires a sophisticated alternate
optimization process, either in the form of \emph{minmax game} or intermediate
\emph{density estimation}. This alternate optimization process is relatively
hard and unstable. In order to avoid such sophisticated alternate optimization,
we propose to learn unsupervised word mapping by directly maximizing the mean
discrepancy between the distribution of transferred embedding and target
embedding. Extensive experimental results show that our proposed model
outperforms competitive baselines by a large margin.
