  We address the problems of multi-domain and single-domain regression based on
distinct and unpaired labeled training sets for each of the domains and a large
unlabeled training set from all domains. We formulate these problems as a
Bayesian estimation with partial knowledge of statistical relations. We propose
a worst-case design strategy and study the resulting estimators. Our analysis
explicitly accounts for the cardinality of the labeled sets and includes the
special cases in which one of the labeled sets is very large or, in the other
extreme, completely missing. We demonstrate our estimators in the context of
removing expressions from facial images and in the context of audio-visual word
recognition, and provide comparisons to several recently proposed multi-modal
learning algorithms.
