Abstract : We study here the problem of estimating the parameters of standard IR models (as BM25 or language models) on new collections without any relevance judgments, by using collections with already available relevance judgements. We propose different query representations that allow mapping queries (with and without relevance judgments, from different collections, potentially in different languages) into a common space. We then introduce a kernel regression approach to learn the parameters of standard IR models individually for each query in the new, unlabeled collection. Our experiments, conducted on standard English and Indian IR collections, show that our approach can be used to efficiently tune, query by query, standard IR models to new collections, potentially written in different languages. In particular, the versions of the standard IR models we obtain not only outperform the versions with default parameters, but can also outperform the versions in which the parameter values have been optimized globally over a set of queries with target relevance judgements.