Monotone Instance Ranking with mira

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In many ranking problems, common sense dictates that the rank assigned to an instance should be increasing (or decreasing) in one or more of the attributes describing it. Consider, for example, the problem of ranking documents with respect to their relevance to a particular query. Typical attributes are counts of query terms in the abstract or title of the document, so it is natural to postulate the existence of an increasing relationship between these counts and document relevance. Such relations between attributes and rank are called monotone. In this paper we present a new algorithm for instance ranking called mira which learns a monotone ranking function from a set of labelled training examples. Monotonicity is enforced by applying the isotonic regression to the training sample, together with an interpolation scheme to rank new data points. This is combined with logistic regression in an attempt to remove unwanted rank equalities. Through experiments we show that mira produces ranking functions having predictive performance comparable to that of a state-of-the-art instance ranking algorithm. This makes mira a valuable alternative when monotonicity is desired or mandatory.