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.