title: Ranking in the algebra of the symmetric group
speaker: Risi Kondor (joint work with Marconi Soares Barbosa)

abstract:
Ranking is hard because implicitly it involves manipulating 
n!-dimensional vectors. We show that if each training example 
only involves k out of the n objects to be ranked, then by Fourier 
analysis on the ranking vectors we can reduce the dimensionality 
of the problem to O(n^{2k}). Moreover, with respect to a natural 
class of kernels on permutations the inner product between two 
ranking vectors can be computed in O((2k)^{2k+2}) time. We demonstrate 
these results by experiments using "SnOB" on real-world data.