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Learning Multiple Tasks with Kernel Methods
- T. Evgeniou, C. Micchelli, M. Pontil
- Mathematics, Computer Science
- J. Mach. Learn. Res.
- 1 December 2005
We study the problem of learning many related tasks simultaneously using kernel methods and regularization. The standard single-task kernel methods, such as support vector machines and regularization… Expand
On Learning Vector-Valued Functions
In this letter, we provide a study of learning in a Hilbert space of vector-valued functions. We motivate the need for extending learning theory of scalar-valued functions by practical considerations… Expand
Learning the Kernel Function via Regularization
We study the problem of finding an optimal kernel from a prescribed convex set of kernels K for learning a real-valued function by regularization. We establish for a wide variety of regularization… Expand
Interpolation of scattered data: Distance matrices and conditionally positive definite functions
- C. Micchelli
- 1 December 1986
Among other things, we prove that multiquadric surface interpolation is always solvable, thereby settling a conjecture of R. Franke.
A Survey of Optimal Recovery
The problem of optimal recovery is that of approximating as effectively as possible a given map of any function known to belong to a certain class from limited, and possibly error-contaminated,… Expand
Using the Refinement Equations for the Construction of Pre-Wavelets II: Powers of Two
We study basic questions of wavelet decompositions associated with multiresolution analysis. A rather complete analysis of multiresolution associated with the solution of a refinement equation is… Expand
Approximation by superposition of a sigmoidal function
In this paper we investigate conditions on the features of a continuous kernel so that it may approximate an arbitrary continuous target function uniformly on any compact subset of the input space. A… Expand
A Spectral Regularization Framework for Multi-Task Structure Learning
Learning the common structure shared by a set of supervised tasks is an important practical and theoretical problem. Knowledge of this structure may lead to better generalization performance on the… Expand