Regularization Networks and Support Vector Machines

By Theodoros Evgeniou, Massimiliano Pontil, Tomaso A. Poggio. 2000

1,338 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Control and Systems Engineering

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Citations in the corpus

Universality, Characteristic Kernels and RKHS Embedding of Measures (2010, methodology): “In the regularization approach to learning (Evgeniou et al., 2000), it is well known that kernel-based algorithms (for classiﬁcation/regression) generally invoke the representer theorem (Kimeldorf and Wahba, 1970; Sch¨olkopf et al., 2001) and learn a function in H that has the representation, where…”
On the mathematical foundations of learning (2001, methodology): “We mention as examples the theory of Neural Networks going back to McCulloch and Pitts [25] and Minsky and Papert [27], the PAC learning of Valiant [40], Statistical Learning Theory as developed by Vapnik [42], and the use of reproducing kernels as in [17] among many other mathematical developments.”
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].”
Optimal Rates for the Regularized Least-Squares Algorithm (2007, background): “We now introduce some basic concepts of statistical learning theory in the regression setting for vector-valued outputs (for details see [32], [15], [24], [6], [20] and references therein).”
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”
Just Interpolate: Kernel "Ridgeless" Regression Can Generalize (2018, background): “[15] Theodoros Evgeniou, Massimiliano Pontil, and Tomaso Poggio.”
Finite-Dimensional Projection for Classification and Statistical Learning (2008, positive): “This algorithm is dubbed kernel projection machine (KPM, originally introduced in [8]).”
The Entire Regularization Path for the Support Vector Machine (2004, background): “By the well-studied properties of such spaces (Wahba, 1990; Evgeniou et al., 1999), the solution to (6) is finite dimensional (even if HK is infinite dimensional), in this case with a representation f (x) = β0 +∑i=1 θiK(x,xi). Consequently (6) reduces to the finite form min β0,θ n ∑ i=1 L[yi,β0 + n ”
The Kernel Least-Mean-Square Algorithm (2008, background): “The significance of an upper bound for the solution norm is well studied by Poggio and Girosi in the context of regularization network theory [14], [26].”
Learning, Regularization and Ill-Posed Inverse Problems (2004, background): “Interestingly, as noted by [12], [8], [2], this is the idea underlying regularization techniques for ill-posed inverse problems [15], [7].”
A note on application of integral operator in learning theory (2009, methodology): “The resurgence of the kernel methods and the study of learning theory from an approximation point of view [5] have motivated a lot of research on this RKHS based regularization scheme [7,13,14,16,19].”
An Efficient Algorithm for Computing the HHSVM and Its Generalizations (2013, neutral): “The ﬁrst dataset Arcene is obtained from UCI Machine Learning Repository (Frank and Asuncion 2010).”
Fingerprint Classification with Combinations of Support Vector Machines (2001, background): “For other important examples of kernel functions used in practice see [5,17].”