On the Consistency of Ranking Algorithms

We present a theoretical analysis of supervised ranking, providing necessary and sufficient conditions for the asymptotic consistency of algorithms based on minimizing a surrogate loss function. We show that many commonly used surrogate losses are inconsistent; surprisingly, we show inconsistency even in low-noise settings. We present a new value-regularized linear loss, establish its consistency under reasonable assumptions on noise, and show that it outperforms conventional ranking losses in a collaborative filtering experiment. The goal in ranking is to order a set of inputs in accordance with the preferences of an individual or a population. In this paper we consider a general formulation of the supervised ranking problem in which each training example consists of a query q, a set of inputs x, sometimes called results, and a weighted graph G representing preferences over the results. The learning task is to discover a function that provides a queryspecific ordering of the inputs t...

• Type: Conference
• Year: 2010
• Where: ICML
• Authors: John Duchi, Lester W. Mackey, Michael I. Jordan
• Keywords: ICML 2010, Loss Function, Machine Learning, Ranking, Supervised Ranking