Browsing AI Memos (1959  2004) by Author "Girosi, Federico"
Now showing items 119 of 19

A Connection Between GRBF and MLP
Maruyama, Minoru; Girosi, Federico; Poggio, Tomaso (19920401)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 ... 
Continuous Stochastic Cellular Automata that Have a Stationary Distribution and No Detailed Balance
Poggio, Tomaso; Girosi, Federico (19901201)Marroquin and Ramirez (1990) have recently discovered a class of discrete stochastic cellular automata with Gibbsian invariant measures that have a nonreversible dynamic behavior. Practical applications include more ... 
Convergence Rates of Approximation by Translates
Girosi, Federico; Anzellotti, Gabriele (19920301)In this paper we consider the problem of approximating a function belonging to some funtion space Î¦ by a linear comination of n translates of a given function G. Ussing a lemma by Jones (1990) and Barron (1991) we show ... 
An Equivalence Between Sparse Approximation and Support Vector Machines
Girosi, Federico (19970501)In the first part of this paper we show a similarity between the principle of Structural Risk Minimization Principle (SRM) (Vapnik, 1982) and the idea of Sparse Approximation, as defined in (Chen, Donoho and Saunders, ... 
Extensions of a Theory of Networks for Approximation and Learning: Dimensionality Reduction and Clustering
Poggio, Tomaso; Girosi, Federico (19900401)The theory developed in Poggio and Girosi (1989) shows the equivalence between regularization and a class of threelayer networks that we call regularization networks or Hyper Basis Functions. These networks are also ... 
Extensions of a Theory of Networks for Approximation and Learning: Outliers and Negative Examples
Girosi, Federico; Poggio, Tomaso; Caprile, Bruno (19900701)Learning an inputoutput mapping from a set of examples can be regarded as synthesizing an approximation of a multidimensional function. From this point of view, this form of learning is closely related to regularization ... 
Forecasting Global Temperature Variations by Neural Networks
Miyano, Takaya; Girosi, Federico (19940801)Global temperature variations between 1861 and 1984 are forecast usingsregularization networks, multilayer perceptrons and linearsautoregression. The regularization network, optimized by stochasticsgradient descent associated ... 
Models of Noise and Robust Estimates
Girosi, Federico (19911101)Given n noisy observations g; of the same quantity f, it is common use to give an estimate of f by minimizing the function Eni=1(gif)2. From a statistical point of view this corresponds to computing the Maximum likelihood ... 
Networks and the Best Approximation Property
Girosi, Federico; Poggio, Tomaso (19891001)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 ... 
A Nondeterministic Minimization Algorithm
Caprile, Bruno; Girosi, Federico (19900901)The problem of minimizing a multivariate function is recurrent in many disciplines as Physics, Mathematics, Engeneering and, of course, Computer Science. In this paper we describe a simple nondeterministic algorithm ... 
Notes on PCA, Regularization, Sparsity and Support Vector Machines
Poggio, Tomaso; Girosi, Federico (19980501)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. ... 
On the Noise Model of Support Vector Machine Regression
Pontil, Massimiliano; Mukherjee, Sayan; Girosi, Federico (19981001)Support Vector Machines Regression (SVMR) is a regression technique which has been recently introduced by V. Vapnik and his collaborators (Vapnik, 1995; Vapnik, Golowich and Smola, 1996). In SVMR the goodness of fit ... 
On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions
Niyogi, Partha; Girosi, Federico (19940201)In this paper, we bound the generalization error of a class of Radial Basis Function networks, for certain well defined function learning tasks, in terms of the number of parameters and number of examples. We show ... 
Parallel and Deterministic Algorithms for MRFs: Surface Reconstruction and Integration
Geiger, Davi; Girosi, Federico (19890501)In recent years many researchers have investigated the use of Markov random fields (MRFs) for computer vision. The computational complexity of the implementation has been a drawback of MRFs. In this paper we derive ... 
Priors Stabilizers and Basis Functions: From Regularization to Radial, Tensor and Additive Splines
Girosi, Federico; Jones, Michael; Poggio, Tomaso (19930601)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 ... 
Some Extensions of the KMeans Algorithm for Image Segmentation and Pattern Classification
Marroquin, Jose L.; Girosi, Federico (19930101)In this paper we present some extensions to the kmeans algorithm for vector quantization that permit its efficient use in image segmentation and pattern classification tasks. It is shown that by introducing state ... 
Sparse Correlation Kernel Analysis and Reconstruction
Papgeorgiou, Constantine P.; Girosi, Federico; Poggio, Tomaso (19980501)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 ... 
Support Vector Machines: Training and Applications
Osuna, Edgar; Freund, Robert; Girosi, Federico (19970301)The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Labs. This new learning algorithm can be seen as an alternative training technique ... 
A Theory of Networks for Appxoimation and Learning
Poggio, Tomaso; Girosi, Federico (19890701)Learning an inputoutput 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 multidimensional function, that ...