Weakly differentiable functions
Weakly differentiable functions
Learning in Neural Networks: Theoretical Foundations
Learning in Neural Networks: Theoretical Foundations
The covering number in learning theory
Journal of Complexity
Semi-Supervised Learning on Riemannian Manifolds
Machine Learning
A theoretical characterization of linear SVM-based feature selection
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Some Properties of Regularized Kernel Methods
The Journal of Machine Learning Research
Model Selection for Regularized Least-Squares Algorithm in Learning Theory
Foundations of Computational Mathematics
Estimation of Gradients and Coordinate Covariation in Classification
The Journal of Machine Learning Research
On complexity issues of online learning algorithms
IEEE Transactions on Information Theory
Capacity of reproducing kernel spaces in learning theory
IEEE Transactions on Information Theory
Gradient learning in a classification setting by gradient descent
Journal of Approximation Theory
Hermite learning with gradient data
Journal of Computational and Applied Mathematics
Online Learning with Samples Drawn from Non-identical Distributions
The Journal of Machine Learning Research
Optimal learning rates for least squares regularized regression with unbounded sampling
Journal of Complexity
An approximation theory approach to learning with l1 regularization
Journal of Approximation Theory
Concentration estimates for learning with unbounded sampling
Advances in Computational Mathematics
Nonparametric sparsity and regularization
The Journal of Machine Learning Research
| Hi-index | 7.29 |
The regularity of functions from reproducing kernel Hilbert spaces (RKHSs) is studied in the setting of learning theory. We provide a reproducing property for partial derivatives up to order s when the Mercer kernel is C^2^s. For such a kernel on a general domain we show that the RKHS can be embedded into the function space C^s. These observations yield a representer theorem for regularized learning algorithms involving data for function values and gradients. Examples of Hermite learning and semi-supervised learning penalized by gradients on data are considered.