An equivalence between sparse approximation and support vector machines
Neural Computation
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Sparseness of support vector machines
The Journal of Machine Learning Research
On Learning Vector-Valued Functions
Neural Computation
Derivative reproducing properties for kernel methods in learning theory
Journal of Computational and Applied Mathematics
Learning from dependent observations
Journal of Multivariate Analysis
Towards a Theoretical Framework for Learning Multi-modal Patterns for Embodied Agents
ICIAP '09 Proceedings of the 15th International Conference on Image Analysis and Processing
Gradient learning in a classification setting by gradient descent
Journal of Approximation Theory
Robustness of reweighted Least Squares Kernel Based Regression
Journal of Multivariate Analysis
Hermite learning with gradient data
Journal of Computational and Applied Mathematics
Classification with Gaussians and Convex Loss
The Journal of Machine Learning Research
When Is There a Representer Theorem? Vector Versus Matrix Regularizers
The Journal of Machine Learning Research
Online Learning with Samples Drawn from Non-identical Distributions
The Journal of Machine Learning Research
On qualitative robustness of support vector machines
Journal of Multivariate Analysis
The consistency analysis of coefficient regularized classification with convex loss
WSEAS Transactions on Mathematics
Bound the learning rates with generalized gradients
WSEAS Transactions on Signal Processing
Kernels for Vector-Valued Functions: A Review
Foundations and Trends® in Machine Learning
A practical use of regularization for supervised learning with kernel methods
Pattern Recognition Letters
Conditional quantiles with varying Gaussians
Advances in Computational Mathematics
| Hi-index | 0.00 |
In regularized kernel methods, the solution of a learning problem is found by minimizing functionals consisting of the sum of a data and a complexity term. In this paper we investigate some properties of a more general form of the above functionals in which the data term corresponds to the expected risk. First, we prove a quantitative version of the representer theorem holding for both regression and classification, for both differentiable and non-differentiable loss functions, and for arbitrary offset terms. Second, we show that the case in which the offset space is non trivial corresponds to solving a standard problem of regularization in a Reproducing Kernel Hilbert Space in which the penalty term is given by a seminorm. Finally, we discuss the issues of existence and uniqueness of the solution. From the specialization of our analysis to the discrete setting it is immediate to establish a connection between the solution properties of sparsity and coefficient boundedness and some properties of the loss function. For the case of Support Vector Machines for classification, we also obtain a complete characterization of the whole method in terms of the Khun-Tucker conditions with no need to introduce the dual formulation.