We consider ordinal classication and instance ranking problems where each attribute is known to have an increasing or decreasing relation with the class label or rank. For example, it stands to reason that the number of query terms occurring in a document has a positive in uence on its relevance to the query. We aim to exploit such monotonicity constraints by using labeled attribute vectors to draw conclusions about the class labels of order related unlabeled ones. Assuming we have a pool of unlabeled attribute vectors, and an oracle that can be queried for class labels, the central problem is to choose a query point whose label is expected to provide the most information. We evaluate dierent query strategies by comparing the number of inferred labels after some limited number of queries, as well as by comparing the prediction errors of models trained on the points whose labels have been determined so far. We present an ecient algorithm to determine the query point preferred by the well-known active learning strategy generalized binary search. This algorithm can be applied to binary classication on incomplete matrix orders. For non-binary classication, we propose to include attribute vectors in the training set whose class labels have not been uniquely determined yet. We perform experiments on articial and real data
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