Mathematical Methods for Supervised Learning

By Ronald A. DeVore, Gerard Kerkyacharian, Dominique Picard, Vladimir N. Temlyakov. 2005

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Citations in the corpus

Density Estimation in Infinite Dimensional Exponential Families (2013, methodology): “…and kernel density estimator appropriate choice of the regularizer) by obtaining minimax lower bounds under the source condition log p 0 ∈ R ( C β ), using the ideas in [10]. depends Second, the proposed estimator depends on the regularization parameter, which in turn on the smoothness scale β .”
Optimal Rates for the Regularized Least-Squares Algorithm (2007, background): “…as in [26], the other one is related to the effective dimension of the marginal probability measure over the input space relative to the chosen kernel; roughly speaking, it counts the number of degrees of freedom associated to the kernel and the marginal measure, available at a given conditioning.”
Optimal Rates for Regularization Operators in Learning Theory (2006, background): “Second, the asymptotic rate of convergence O m− r 2r+s of f ls z̃,λ − fH ρ, is optimal in the minimax sense of [11, 4].”
DISCRETIZATION ERROR ANALYSIS FOR TIKHONOV REGULARIZATION (2006, background): “As noticed by many authors, the theory is strongly related to the function approximation [10, 35] and the non-parametric regression [15].”
Model selection via testing: an alternative to (penalized) maximum likelihood estimators (2006, background): “This would involve the comparison of our upper bounds with lower bounds based on dimensional arguments, as in [8,10,11,72,69] or [26].”
On Early Stopping in Gradient Descent Learning (2007, background): “Some minimax lower rate [DeVore, Kerkyacharian, Picard, and Temlyakov 2004, Temlyakov 2004] and individual lower rate [Caponnetto and De Vito 2005], suggest that for r > 0 the convergence rate O ( m − r/ (2 r +1) ) is optimal in both senses, which has been achieved by the usual regularized least…”