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We address the problems of multi-domain and single-domain regression based on distinct labeled training sets for each of the domains and a large unlabeled training set from all domains. We formulate these problems as ones of 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 audio-visual word recognition and provide comparisons to several recently proposed multi-modal learning algorithms.