Regularization theory and neural networks architectures
Neural Computation
Machine Learning
An equivalence between sparse approximation and support vector machines
Neural Computation
From regularization operators to support vector kernels
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
On different facets of regularization theory
Neural Computation
A Theory of Networks for Approximation and Learning
A Theory of Networks for Approximation and Learning
Error Estimates for Approximate Optimization by the Extended Ritz Method
SIAM Journal on Optimization
Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization (Mps-Siam Series on Optimization 6)
Simpler knowledge-based support vector machines
ICML '06 Proceedings of the 23rd international conference on Machine learning
Proximal Knowledge-based Classification
Statistical Analysis and Data Mining
Learning with generalization capability by kernel methods of bounded complexity
Journal of Complexity
ICONIP'11 Proceedings of the 18th international conference on Neural Information Processing - Volume Part II
Nonlinear Knowledge-Based Classification
IEEE Transactions on Neural Networks
Learning with boundary conditions
Neural Computation
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Supervised learning is investigated, when the data are represented not only by labeled points but also labeled regions of the input space. In the limit case, such regions degenerate to single points and the proposed approach changes back to the classical learning context. The adopted framework entails the minimization of a functional obtained by introducing a loss function that involves such regions. An additive regularization term is expressed via differential operators that model the smoothness properties of the desired input/output relationship. Representer theorems are given, proving that the optimization problem associated to learning from labeled regions has a unique solution, which takes on the form of a linear combination of kernel functions determined by the differential operators together with the regions themselves. As a relevant situation, the case of regions given by multi-dimensional intervals (i.e., ''boxes'') is investigated, which models prior knowledge expressed by logical propositions.