• Publications
  • Influence
Learning Multiple Tasks with Kernel Methods
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 regularizationExpand
  • 825
  • 91
  • PDF
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 considerationsExpand
  • 406
  • 74
  • PDF
Stationary Subdivision
  • 660
  • 54
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 regularizationExpand
  • 392
  • 35
  • PDF
Interpolation of scattered data: Distance matrices and conditionally positive definite functions
Among other things, we prove that multiquadric surface interpolation is always solvable, thereby settling a conjecture of R. Franke.
  • 1,049
  • 25
  • PDF
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
  • 310
  • 24
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 isExpand
  • 308
  • 19
  • PDF
Approximation by superposition of a sigmoidal function
  • 424
  • 18
Universal Kernels
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. AExpand
  • 314
  • 17
  • PDF
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 theExpand
  • 226
  • 17
  • PDF