nips nips2005 nips2005-205 nips2005-205-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Sham M. Kakade, Matthias W. Seeger, Dean P. Foster
Abstract: We present a competitive analysis of some non-parametric Bayesian algorithms in a worst-case online learning setting, where no probabilistic assumptions about the generation of the data are made. We consider models which use a Gaussian process prior (over the space of all functions) and provide bounds on the regret (under the log loss) for commonly used non-parametric Bayesian algorithms — including Gaussian regression and logistic regression — which show how these algorithms can perform favorably under rather general conditions. These bounds explicitly handle the infinite dimensionality of these non-parametric classes in a natural way. We also make formal connections to the minimax and minimum description length (MDL) framework. Here, we show precisely how Bayesian Gaussian regression is a minimax strategy. 1