The problem of ranking is to predict or to guess the ordering between objects on the basis of their observed features. In this paper we consider ranking estimators that minimize the empirical convex risk. We prove generalization bounds for the excess risk of such estimators with rates that are faster than 1 √n . We apply our results to commonly used ranking algorithms, for instance boosting or ...

The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn a ranking rule for deciding, among two instances, which one is “better,” with minimum ranking risk. Since the natural estimates of the risk are of the form o...

This paper concerns document ranking in information retrieval. In information retrieval systems, the widely accepted probability ranking principle (PRP) suggests that, for optimal retrieval, documents should be ranked in order of decreasing probability of relevance. In this paper, we present a new document ranking paradigm, arguing that a better, more general solution is to optimize top-n ranke...

This study aimed to analyze the impact of key causes external and internal risk on supply chains. The basic most probable are listed, based literature research interviews with representatives metal industry. analysis was carried out by semiquantitative assessment using maps. relationship between probability an event occurrence its chains tested. postulates that factors can be controlled through...

We address the following seemingly simple question: what is the Bayes-optimal scorer for a bipartite ranking risk? The answer to this question helps elucidate the relationship between bipartite ranking and other established learning problems. We show that the answer is non-trivial in general, but may be easily determined for certain special cases using the theory of proper losses. Our analysis ...

A general model is proposed for studying ranking problems. We investigate learning methods based on empirical minimization of the natural estimates of the ranking risk. The empirical estimates are of the form of a U -statistic. Inequalities from the theory of U -statistics and U processes are used to obtain performance bounds for the empirical risk minimizers. Convex risk minimization methods a...