  We use transductive regression techniques to learn mappings between source
and target features of given parallel corpora and use these mappings to
generate machine translation outputs. We show the effectiveness of $L_1$
regularized regression (\textit{lasso}) to learn the mappings between sparsely
observed feature sets versus $L_2$ regularized regression. Proper selection of
training instances plays an important role to learn correct feature mappings
within limited computational resources and at expected accuracy levels. We
introduce \textit{dice} instance selection method for proper selection of
training instances, which plays an important role to learn correct feature
mappings for improving the source and target coverage of the training set. We
show that $L_1$ regularized regression performs better than $L_2$ regularized
regression both in regression measurements and in the translation experiments
using graph decoding. We present encouraging results when translating from
German to English and Spanish to English. We also demonstrate results when the
phrase table of a phrase-based decoder is replaced with the mappings we find
with the regression model.
