A localized prediction model for statistical machine translation
Christoph Tillmann, Tong Zhang
ACL 2005
Kernel methods can embed finite-dimensional data into infinite-dimensional feature spaces. In spite of the large underlying feature dimensionality, kernel methods can achieve good generalization ability. This observation is often wrongly interpreted, and it has been used to argue that kernel learning can magically avoid the "curse-of-dimensionality" phenomenon encountered in statistical estimation problems. This letter shows that although using kernel representation, one can embed data into an infinite-dimensional feature space; the effective dimensionality of this embedding, which determines the learning complexity of the underlying kernel machine, is usually small. In particular, we introduce an algebraic definition of a scale-sensitive effective dimension associated with a kernel representation. Based on this quantity, we derive upper bounds on the generalization performance of some kernel regression methods. Moreover, we show that the resulting convergent rates are optimal under various circumstances. © 2005 Massachusetts Institute of Technology.
Christoph Tillmann, Tong Zhang
ACL 2005
Tong Zhang, Fred Damerau, et al.
CoNLL 2003
Jane Cullum, Albert Ruehli, et al.
IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing
Tong Zhang
JMLR