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Summary: Journal of Machine Learning Research 10 (2009) 441-474 Submitted 10/07; Revised 12/08; Published 2/09
Generalization Bounds for Ranking Algorithms
via Algorithmic Stability
Shivani Agarwal SHIVANI@MIT.EDU
Department of Electrical Engineering & Computer Science
Massachusetts Institute of Technology
Cambridge, MA 02139, USA
Partha Niyogi NIYOGI@CS.UCHICAGO.EDU
Departments of Computer Science and Statistics
University of Chicago
Chicago, IL 60637, USA
Editor: Andre Elisseeff
Abstract
The problem of ranking, in which the goal is to learn a real-valued ranking function that induces a
ranking or ordering over an instance space, has recently gained much attention in machine learning.
We study generalization properties of ranking algorithms using the notion of algorithmic stability;
in particular, we derive generalization bounds for ranking algorithms that have good stability prop-
erties. We show that kernel-based ranking algorithms that perform regularization in a reproducing
kernel Hilbert space have such stability properties, and therefore our bounds can be applied to these
algorithms; this is in contrast with generalization bounds based on uniform convergence, which in
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