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Transductive methods are useful in prediction problems when the trainingdataset is composed of a large number of unlabeled observations and a smallernumber of labeled observations. In this paper, we propose an approach fordeveloping transductive prediction procedures that are able to take advantageof the sparsity in the high dimensional linear regression. More precisely, wedefine transductive versions of the LASSO and the Dantzig Selector . Theseprocedures combine labeled and unlabeled observations of the training datasetto produce a prediction for the unlabeled observations. We propose anexperimental study of the transductive estimators, that shows that they improvethe LASSO and Dantzig Selector in many situations, and particularly in highdimensional problems when the predictors are correlated. We then providenon-asymptotic theoretical guarantees for these estimation methods.Interestingly, our theoretical results show that the Transductive LASSO andDantzig Selector satisfy sparsity inequalities under weaker assumptions thanthose required for the "original" LASSO.

Transductive versions of the LASSO and the Dantzig Selector