Regularization Algorithms for Learning That Are Equivalent to Multilayer Networks

By Tomaso A. Poggio, Federico Girosi. 1990

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Recent advances in surrogate-based optimization (2009, background): “Perhaps the easiest way around this is the introduction of added model flexibility in the form of the regularization parameter λ [60].”
An Introduction to Boosting and Leveraging (2002, background): “[103, 186, 143, 43]) is mandatory if overfitting is to be avoided (cf.”
Performance evaluation of two different neural network and particle swarm optimization methods for prediction of discharge capacity of modified triangular side weirs (2014, background): “Radial basis neural networks (RBNN) [39,40] are formed of two layers.”
Neural Networks and the Bias/Variance Dilemma (1992, background): “" Poggio and Girosi (1990) have shown how splines and related estimators can be computed with multilayer networks.”
Learning of Visuomotor Transformations for Vectorial Planning of Reaching Trajectories (2000, background): “multiple-layer perceptions (Poggio and Gorosi, 1990).”
Prescribed performance adaptive control of SISO feedback linearizable systems with disturbances (2008, background): “The regressor terms may contain high order connections of sigmoid functions [17], radial basis functions (RBFs) with fixed centers and widths [18]–[20], shifted sigmoids [21], [22], thus forming high order neural networks (HONNs), RBFs and Shifted Sigmoidal Neural Networks, respectively.”
Data-driven Soft Sensors in the process industry (2009, background): “Among the large number of ANN variants mentioned above, the most common, in the process industry as well as in general, are the feed-forward networks, like the Multi-Layer Perceptron (MLP) (Bishop, 1995) and the Radial-Basis Function Network (RBFN) (Poggio and Girosi, 1990).”
Adaptive computation and machine learning (1998, background): “A number of popular algorithms such as support vector machines (SVMs), ridge regression, splines, and radial basis functions may be broadly interpreted as regularization algorithms with different empirical cost functions and complexity measures in an appropriately chosen reproducing kernel Hilbert s”
Maximally fault tolerant neural networks (1992, methodology): “[3] T. Poggio and F. Girosi, "Regularization algorithms for learning that are equivalent to multilayer networks," Science, vol .”
Stability and generalization (2002, background): “In order to do this, we need some standard definitions about convex functions which we deferred to Appendix C where most of the material can be found in Rockafellar (1970) and in Gordon (1999).”
3D Object Recognition: Symmetry and Virtual Views (1992, background): “In the more general HBF scheme the number of units, that is templates, used during recognition may be less than the number of training views and in addition the appropriate similarity metric is found automatically during learning (see Poggio and Girosi, 1990).”
Evolving spiking neural networks for audiovisual information processing (2010, background): “The results of these individual classifiers are connected to the input of a new integrative module based on HyperBF networks (Poggio & Girosi, 1990).”