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Priors Stabilizers and Basis Functions: From Regularization to Radial, Tensor and Additive Splines
(1993-06-01)
We had previously shown that regularization principles lead to approximation schemes, as Radial Basis Functions, which are equivalent to networks with one layer of hidden units, called Regularization Networks. In this ...
Sparse Correlation Kernel Analysis and Reconstruction
(1998-05-01)
This paper presents a new paradigm for signal reconstruction and superresolution, Correlation Kernel Analysis (CKA), that is based on the selection of a sparse set of bases from a large dictionary of class- specific basis ...
Networks and the Best Approximation Property
(1989-10-01)
Networks can be considered as approximation schemes. Multilayer networks of the backpropagation type can approximate arbitrarily well continuous functions (Cybenko, 1989; Funahashi, 1989; Stinchcombe and White, 1989). We ...
Extensions of a Theory of Networks for Approximation and Learning: Outliers and Negative Examples
(1990-07-01)
Learning an input-output mapping from a set of examples can be regarded as synthesizing an approximation of a multi-dimensional function. From this point of view, this form of learning is closely related to regularization ...
A Theory of Networks for Appxoimation and Learning
(1989-07-01)
Learning an input-output mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multi-dimensional function, that ...
Notes on PCA, Regularization, Sparsity and Support Vector Machines
(1998-05-01)
We derive a new representation for a function as a linear combination of local correlation kernels at optimal sparse locations and discuss its relation to PCA, regularization, sparsity principles and Support Vector Machines. ...
Continuous Stochastic Cellular Automata that Have a Stationary Distribution and No Detailed Balance
(1990-12-01)
Marroquin and Ramirez (1990) have recently discovered a class of discrete stochastic cellular automata with Gibbsian invariant measures that have a non-reversible dynamic behavior. Practical applications include more ...
Extensions of a Theory of Networks for Approximation and Learning: Dimensionality Reduction and Clustering
(1990-04-01)
The theory developed in Poggio and Girosi (1989) shows the equivalence between regularization and a class of three-layer networks that we call regularization networks or Hyper Basis Functions. These networks are also ...
A Connection Between GRBF and MLP
(1992-04-01)
Both multilayer perceptrons (MLP) and Generalized Radial Basis Functions (GRBF) have good approximation properties, theoretically and experimentally. Are they related? The main point of this paper is to show that for ...