Networks for approximation and learning

By Tomaso A. Poggio, Federico Girosi. 1990

Subfields: Model Architectures, Statistical Learning Theory

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Citations in the corpus

Deep Learning in Finance (2016, background): “See Kolmorogov (1957), Lorenz (1976), Gallant and White (1988), Hornik et al. (1989), and Poggio and Girosi (1990) for further discussion.”
Kernel methods in machine learning (2007, neutral): “Our exposition will be informal (see also Poggio and Girosi [109] and Smola et al. [127]), and we will implicitly assume that all integrals are over Rd and exist, and that the operators are well defined.”
Hidden physics models: Machine learning of nonlinear partial differential equations (2017, background): “Gaussian processes are among a class of methods known as kernel machines (see [8, 9, 10]) and are analogous to regularization approaches (see [11, 12, 13]).”
Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations (2017, background): “Moreover, Gaussian processes are among a class of methods known as kernel machines (see [31, 36, 37]) and are analogous to regularization approaches (see [21, 34, 35]).”
Machine learning of linear differential equations using Gaussian processes (2017, background): “Moreover, Gaussian processes are among a class of methods known as kernel machines (see [51,44,49]) and have analogies with regularization approaches (see [47,48,36]).”
Prior Learning and Gibbs Reaction-Diffusion (1997, unknown): “The first is often used for image coding [35], and the second is a special case of the learning scheme using radial basis functions (RBF) [27].”
Hierarchical learning : theory with applications in speech and vision (2009, background): “We believe that this argument cannot be used to demonstrate that one layer of computations (whatever they may be) is inferior to multiple layers: one could consider a single layer of radial basis functions with different bandwidths (see “Generalized RBF Networks” in [78]).”
Deep Mixture Generative Autoencoders (2021, methodology): “RBF networks have been shown to have universal approximation properties [5]–[7].”
Value Regularization and Fenchel Duality (2007, methodology): “We will show that the “natural” algorithm suggested by the Nyström approximation is in fact the subset of regressors method (Poggio and Girosi, 1990; Luo and Wahba, 1997), as opposed to the Nyström method.9 In contrast, the Nyström method essentially makes an unwarranted (and incorrect)…”
Information Theory, Inference, and Learning Algorithms (2004, background): “Methods for reducing the complexity of data modelling with Gaussian processes remain an active research area (Poggio and Girosi, 1990; Luo and Wahba, 1997; Tresp, 2000; Williams and Seeger, 2001; Smola and Bartlett, 2001; Rasmussen, 2002; Seeger et al., 2003; Opper and Winther, 2000).”
Mapping a Manifold of Perceptual Observations (1997, methodology): “Having found a number of corresponding pairs of images and feature vectors , it is easy to learn an explicit inverse mapping 1 : from low-dimensional feature space to high-dimensional observation space, using generic smooth interpolation techniques such as generalized radial basis function (GRBF) ne”
Generalization Properties of Learning with Random Features (2016, background): “Among others, one-hidden layer networks [3], or RBF networks [4], are examples of classical approaches considering these models.”
High-dimensional geometry of population responses in visual cortex (2018, unknown): “To understand how the kernel function determines downstream learning, it is useful to adopt the “function space” description of kernel learning systems [14, 15].”
Kernel Pooling for Convolutional Neural Networks (2017, unknown): “The Taylor expansion of Gaussian RBF kernel [32] can be expressed as: KRBF (x,y) = exp (− γ‖x− y‖2) = exp (− γ(‖x‖2 + ‖y‖2 − 2x y))”
Bayesian Gaussian process models : PAC-Bayesian generalisation error bounds and sparse approximations (2003, methodology): “In general (see [202, 145]), we make use of the duality between a RKHS and a regularisation (pseudodifferential) operator P on L2(μ).”
On-Line Learning Fokker-Planck Machine (1998, methodology): “Like (14) this algorithm can be implemented with vector updates, avoiding the storage of matrices.”