Online regression competitive with reproducing kernel Hilbert spaces(学习资料)资料.pdf

On-line regression competitive with reproducing kernel Hilbert spaces 6 0 0 Vladimir Vovk 2 vovk@cs.rhul.ac.uk n a J 4 February 1, 2008 2 ] Abstract G We consider the problem of on-line prediction of real-valued labels, L assumed bounded in absolute value by a known constant, of new objects . s from known labeled objects. The prediction algorithm’s performance is c measured by the squared deviation of the predictions from the actual [ labels. No stochastic assumptions are made about the way the labels 2 and objects are generated. Instead, we are given a benchmark class of v prediction rules some of which are hoped to produce good predictions. 8 We show that for a wide range of infinite-dimensional benchmark classes 5 one can construct a prediction algorithm whose cumulative loss over the 0 first N examples does not exceed the cumulative loss of any prediction 1 rule in the class plus O(√N ); the main differences from the known results 1 are that we do not impose any upper bound on the norm of the considered 5 prediction rules and that we achieve an optimal leading term in t