Learning With Kernels: Support Vector Machines, Regularization, Optimization, and Beyond

By Christopher K. I. Williams. 2001

1,460 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistical Learning Theory

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Citations in the corpus

Kernel-Based Just-In-Time Learning for Passing Expectation Propagation Messages (2015, methodology): “In principle, during the initial batch training, the operator can perform cross validation for parameter selection; however for simplicity we set the kernel parameters according to the median heuristic [Schölkopf and Smola, 2002].”
Computing functions of random variables via reproducing kernel Hilbert space representations (2015, neutral): “corresponds to a kernel density estimator in the input domain [33, 32], provided the kernel is nonnegative and integrates to 1.”
Random Feature Maps for Dot Product Kernels (2012, background): “However Vovk’s kernels are seldom used in practice since they are expected to have poor generalization properties due to their flat spectrum as noted by Schölkopf and Smola (2002).”
Machine learning unifies the modeling of materials and molecules (2017, positive): “We trained a kernel support vector machine (SVM) ( 31 , 32 ) for each of the 102 receptors listed in the DUD-E to predict whether or not each candidate molecule binds to the corresponding polypeptide.”
Bilinear CNN Models for Fine-Grained Visual Recognition (2015, methodology): “= jj2) inspired by [47]. This improves performance in practice (see our earlier work [37] for an evaluation of the effect of normalization). For classiﬁcation we use logistic regression or linear SVM [55]. Although this can be replaced with an arbitrary multi-layer network, we found that linear mode”
Visual Causal Feature Learning (2014, background): “A similar class of metrics is induced by positivedefinite kernels that shift members of I into an implicit high-dimensional vector space (Schölkopf and Smola, 2002).”
Hidden physics models: Machine learning of nonlinear partial differential equations (2017, background): “y can be viewed as a prior on one-layer feed-forward Bayesian neural networks with an innite number of hidden units [7]. 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]). 3From a theoretical point ”
DART: Noise Injection for Robust Imitation Learning (2017, methodology): “ R;j˘) | {z } Loss ; which corresponds to the covariate shift and the standard loss. In this work, we focus on minimizing the covariate shift. For references on how to minimize the standard loss see [16]. In the next section, we will show how noise injection can be used to reduce covariate shift. 4 ”
Biological Sequence Modeling with Convolutional Kernel Networks (2017, neutral): “Kernel-based methods [Schölkopf and Smola, 2002] have often been used for this task.”
Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations (2017, background): “abilistic workow that returns robust posterior variance estimates, which quantify uncertainty in a natural way. Moreover, Gaussian processes are among a class of methods known as kernel machines (see [16,17,18]) and are analogous to regularization approaches (see [19,20,21]). They can also be viewed”
Machine learning of linear differential equations using Gaussian processes (2017, background): “babilistic workow that returns robust posterior variance estimates which quantify uncertainty in a natural way. Moreover, Gaussian processes are among a class of methods known as kernel machines (see [6,7,8]) and have analogies with regularization approaches (see [9,10,11]). However, they are distin”
Sub-Sampled Newton Methods II: Local Convergence Rates (2016, positive): “siﬁcation, regression, or other tasks. The vast majority of text books and articles introducing SVM very brieﬂy state the the primal optimization problem, and then go directly to the dual formulation [57, 11, 50]. Primal optimizations of linear SVMs have already been studied by [28, 15, 34]. This is”
An introduction to domain adaptation and transfer learning (2018, methodology): “s function that pulls them maximally apart. In practice, kernel functions are used, 18 W.M. Kouw, M. Loog which, under certain conditions, are able to approximateany continuousfunction arbitrary well [5,172,174,22]. The empirical discrepancy measure, including the reweighed source samples, can be ex”
Support Vector Machines Used to Estimate the Battery State of Charge (2013, methodology): “, linear, polynomial, sigmoid, or radial basis) and the base algorithm [13].”
An Equivalence between the Lasso and Support Vector Machines (2013, background): “[4, 37] have shown that the VC-dimension of an SVM, a measure of “difficulty” for the classifier, is always lower than D 2 σ2 .”