The connection between regularization operators and support vector kernels

By Alex Smola, Bernhard Schölkopf, K. Müller. 1998

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Fastfood: Approximate Kernel Expansions in Loglinear Time (2014, background): “This allows us to identify P † P from k and vice versa (Smola et al., 1998a; Girosi, 1998; Girosi et al., 1995; Girosi and Anzellotti, 1993; Wahba, 1990).”
Robustness and Regularization of Support Vector Machines (2008, background): “…the regularization term restricts the complexity of the classiﬁer, hence the deviation of the testing error and the training error is controlled (see Smola et al., 1998; Evgeniou et al., 2000; Bartlett and Mendelson, 2002; Koltchinskii and Panchenko, 2002; Bartlett et al., 2005, and references…”
Exploring Generalization in Deep Learning (2017, neutral): “For linear models, norms and margin-based measures, and not the number of parameters, are commonly used for capacity control [5, 9, 25].”
Stronger generalization bounds for deep nets via a compression approach (2018, methodology): “Clearly, deep nets trained on real-life data have some properties that reduce eﬀective capacity, but identifying them has proved diﬃcult —at least in a quantitative way that yields sample size upper bounds similar to classical analyses in simpler models such as SVMs Bartlett and Mendelson [2002], Ev”
Kernel methods in machine learning (2007, neutral): “[127]), and we will implicitly assume that all integrals are over Rd and exist, and that the operators are well defined.”
Regularized Principal Manifolds (1999, methodology): “Using the results of [9] regarding the connection between regularization operators and kernels it appears suitable to choose a kernel expansion of f matching the regularization operator P , i.”
Kernels and Regularization on Graphs (2003, methodology): “Kernels are obtained by solving the self-consistency condition [Smola et al., 1998] 〈k(x, ·), Pk(x, ·)〉 = k(x, x) .”
Wavelet support vector machine (2004, background): “Translation invariant kernels, i.e., derived in [9] are admissive SV kernels if they satisfy Mercer’s condition.”
Deep Neural Networks Rival the Representation of Primate IT Cortex for Core Visual Object Recognition (2014, methodology): “As suggested by [30], we utilize the Gaussian kernel because this kernel implies a smoothness of the task of interest in the input space [67] and does not bias against representations that may be more adapted to non-linear regression functions.”
Learning the Kernel with Hyperkernels (2005, background): “2 Hyperkernels Invariant to Translation Another approach to constructing hyperkernels is via an extension of a result due to Smola et al. (1998) concerning the Fourier transform of translation invariant kernels.”
Advances in Large Margin Classifiers (2000, methodology): “…Large Margin Classifiers class of functions that the estimate is chosen from are intimately related (Girosi et al., 1993; Smola and Schölkopf, 1998a; Smola et al., 1998): the SV algorithm is equivalent to minimizing the regularized risk Rreg(f) on the set of functions f(x) = ∑ i αik(xi,x) + b,…”