The nature of statistical learning theory
The nature of statistical learning theory
Bayesian Classification With Gaussian Processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Learning from Data: Concepts, Theory, and Methods
Learning from Data: Concepts, Theory, and Methods
Autonomous Driving Goes Downtown
IEEE Intelligent Systems
Kernel partial least squares regression in reproducing kernel hilbert space
The Journal of Machine Learning Research
On the algorithmic implementation of multiclass kernel-based vector machines
The Journal of Machine Learning Research
Regularized multi--task learning
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
On Learning Vector-Valued Functions
Neural Computation
Some Properties of Regularized Kernel Methods
The Journal of Machine Learning Research
Object correspondence as a machine learning problem
ICML '05 Proceedings of the 22nd international conference on Machine learning
On Learning Vector-Valued Functions
Neural Computation
2005 Special Issue: Learning protein secondary structure from sequential and relational data
Neural Networks - Special issue on neural networks and kernel methods for structured domains
Feature space perspectives for learning the kernel
Machine Learning
Learning Coordinate Covariances via Gradients
The Journal of Machine Learning Research
Estimation of Gradients and Coordinate Covariation in Classification
The Journal of Machine Learning Research
Learning Equivariant Functions with Matrix Valued Kernels
The Journal of Machine Learning Research
A transductive framework of distance metric learning by spectral dimensionality reduction
Proceedings of the 24th international conference on Machine learning
Kernels, regularization and differential equations
Pattern Recognition
Discriminatively regularized least-squares classification
Pattern Recognition
The Journal of Machine Learning Research
Convex multi-task feature learning
Machine Learning
Elastic-net regularization in learning theory
Journal of Complexity
Expert Systems with Applications: An International Journal
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
Reproducing kernel banach spaces for machine learning
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Image and Video Colorization Using Vector-Valued Reproducing Kernel Hilbert Spaces
Journal of Mathematical Imaging and Vision
When Is There a Representer Theorem? Vector Versus Matrix Regularizers
The Journal of Machine Learning Research
Reproducing Kernel Banach Spaces for Machine Learning
The Journal of Machine Learning Research
Vector field learning via spectral filtering
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part I
Kernel-based learning from infinite dimensional 2-way tensors
ICANN'10 Proceedings of the 20th international conference on Artificial neural networks: Part II
Using landmarks as a deformation prior for hybrid image registration
DAGM'11 Proceedings of the 33rd international conference on Pattern recognition
Multi-platform gene-expression mining and marker gene analysis
International Journal of Data Mining and Bioinformatics
Kernel-Based Methods for Vector-Valued Data with Correlated Components
SIAM Journal on Scientific Computing
Expert Systems with Applications: An International Journal
Refinement of operator-valued reproducing kernels
The Journal of Machine Learning Research
Kernels for Vector-Valued Functions: A Review
Foundations and Trends® in Machine Learning
Learning the coordinate gradients
Advances in Computational Mathematics
A generic model of multi-class support vector machine
International Journal of Intelligent Information and Database Systems
Vector-valued reproducing kernel Banach spaces with applications to multi-task learning
Journal of Complexity
Finite rank kernels for multi-task learning
Advances in Computational Mathematics
Learning output kernels for multi-task problems
Neurocomputing
Regularized vector field learning with sparse approximation for mismatch removal
Pattern Recognition
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In this letter, we provide a study of learning in a Hilbert space of vectorvalued functions. We motivate the need for extending learning theory of scalar-valued functions by practical considerations and establish some basic results for learning vector-valued functions that should prove useful in applications. Specifically, we allow an output space Y to be a Hilbert space, and we consider a reproducing kernel Hilbert space of functions whose values lie in Y. In this setting, we derive the form of the minimal norm interpolant to a finite set of data and apply it to study some regularization functionals that are important in learning theory. We consider specific examples of such functionals corresponding to multiple-output regularization networks and support vector machines, for both regression and classification. Finally, we provide classes of operator-valued kernels of the dot product and translation-invariant type.