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Proceedings of the 18th Annual Conference on Learning Theory, 2005 Learnability of Bipartite Ranking Functions
 

Summary: Proceedings of the 18th Annual Conference on Learning Theory, 2005
Learnability of Bipartite Ranking Functions
Shivani Agarwal and Dan Roth
Department of Computer Science
University of Illinois at Urbana-Champaign
201 N. Goodwin Avenue, Urbana, IL 61801, USA
{sagarwal,danr}@cs.uiuc.edu
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 attention in machine learning. We define a model of learnability
for ranking functions in a particular setting of the ranking problem known as the
bipartite ranking problem, and derive a number of results in this model. Our first
main result provides a sufficient condition for the learnability of a class of ranking
functions F: we show that F is learnable if its bipartite rank-shatter coefficients,
which measure the richness of a ranking function class in the same way as do the
standard VC-dimension related shatter coefficients (growth function) for classes
of classification functions, do not grow too quickly. Our second main result gives
a necessary condition for learnability: we define a new combinatorial parameter
for a class of ranking functions F that we term the rank dimension of F, and
show that F is learnable only if its rank dimension is finite. Finally, we investigate

  

Source: Agarwal, Shivani - Department of Computer Science and Automation, Indian Institute of Science, Bangalore

 

Collections: Computer Technologies and Information Sciences