U-统计量的排序和经验极小化
Ranking and empirical minimization of U-statistics
摘要：
对实例进行排名/排序的问题，而不是简单地对它们进行分类，最近在机器学习中受到了很多关注。在本文中，我们制定了严格的统计框架中的排名问题。目标是学习一个排名规则，用于在两个实例中决定哪一个“更好”，同时排名风险最小。由于风险的自然估计是U-统计量的形式，U-过程理论的结果需要调查的经验风险最小化的一致性。我们特别建立了退化U-过程的尾部不等式，并将其应用于表明在特定的噪声假设下可以实现快速收敛，就像在分类中一样。凸风险最小化方法也进行了研究。
英文摘要：
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 of a U-statistic, results of the theory of U-processes are required for investigating the consistency of empirical risk minimizers. We establish in particular a tail inequality for degenerate U-processes, and apply it for showing that fast rates of convergence may be achieved under specific noise assumptions, just like in classification. Convex risk minimization methods are also studied.
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