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- Theodoros Evgeniou, Charles A. Micchelli, Massimiliano Pontil
- Journal of Machine Learning Research
- 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 regularizationâ€¦ (More)

Among other things, we prove that multiquadric surface interpolation is always solvable, thereby settling a conjecture of R. Franke.

- Charles A. Micchelli, Massimiliano Pontil
- Neural Computation
- 2005

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 considerationsâ€¦ (More)

- Charles A. Micchelli, Massimiliano Pontil
- Journal of Machine Learning Research
- 2005

We study the problem of finding an optimal kernel from a prescr ibed convex set of kernels K for learning a real-valued function by regularization. We esta blish for a wide variety of regularizationâ€¦ (More)

- Charles A. Micchelli, Massimiliano Pontil
- NIPS
- 2004

This paper provides a foundation for multiâ€“task learning using reproducing kernel Hilbert spaces of vectorâ€“valued functions. In this setting, the kernel is a matrixâ€“valued function. Some explicitâ€¦ (More)

We study the problem of learning a kernel which minimizes a regularization error functional such as that used in regularization networks or support vector machines. We consider this problem when theâ€¦ (More)

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 theâ€¦ (More)

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 isâ€¦ (More)

- Rong-Qing Jia, A. U.S., Charles A. Micchelli
- 1992

We investigate linear independence of integer translates of a finite number of compactly supported functions in two cases. In the first case there are no restrictions on the coefficients that mayâ€¦ (More)

We study the problem of learning a sparse linear regression v ector under additional conditions on the structure of its sparsity pattern. We present a family of convex penalty functions, which encodeâ€¦ (More)