Learning with Kernels

By 유정완. 2011

3,600 citations recorded by the source corpus.

Subfields: Optimization & Training, Statistical Learning Theory

How researchers see this paper

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

In Optimization & Training

In Statistical Learning Theory

Citations in the corpus

Toward Causal Representation Learning (2021, background): “1The present paper expands [221], leading to partial text overlap.”
Taking Advantage of Multitask Learning for Fair Classification (2018, background): “The generality of this approach comes from the general form of the feature mapping ϕ : X×S→ H which may be implicitly defined by a kernel function, see e.g. [33 34] and references therein.”
Towards Causal Representation Learning (2021, background): “Such algorithms do exist, for instance, nearest neighbor classifiers, support vector machines, and neural networks [257, 217, 239, 66].”
On the Fairness of Causal Algorithmic Recourse (2020, methodology): “We consider linear and nonlinear logistic regression (LR), and different support vector machines (SVMs; Schölkopf and Smola 2002) (for ease of comparison with Gupta et al.”
Causality for Machine Learning (2019, methodology): “Such algorithms do exist, for instance nearest neighbor classifiers and Support Vector Machines (Vapnik, 1998; Schölkopf and Smola, 2002; Steinwart and Christmann, 2008).”
Causal Regularization (2019, neutral): “, Xd) via appropriate regression models is among the classical problems of machine learning [1].”
Behind Distribution Shift: Mining Driving Forces of Changes and Causal Arrows (2017, positive): “We tackle the above two problems by using kernels [7] and accordingly propose a method called Nonstationary Driving Force Estimation (NoDFEs) of causal modules.”
Computing functions of random variables via reproducing kernel Hilbert space representations (2015, positive): “It was pointed out that the kernel map of a set of points corresponds to a kernel density estimator in the input domain (Schölkopf and Smola 2002; Schölkopf et al. 2001), provided the kernel is nonnegative and integrates to 1.”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, background): “As covariance function for HSIC, we use the popular Gaussian kernel: κ` : (x, x ′) 7→ exp ( −(x− x ′)2 `2 ) , with bandwidths selected by the median heuristic (Schölkopf and Smola, 2002), i.e., we take ˆ̀(u) := median{‖ui − uj‖ : 1 ≤ i j ≤ N, ‖ui − uj‖ 6= 0}, and similarly for ˆ̀(v).”
Fastfood: Approximate Kernel Expansions in Loglinear Time (2014, background): “For a detailed discussion of spectral properties for a broad range of kernels see e.g. (Smola, 1998).”
Nonparametric Independence Testing for Small Sample Sizes (2014, methodology): “From FCOSE to HSIC The Flexible Covariance Shrinkage Estimator is derived by relying on the Representer theorem, see [Scholkopf and Smola, 2002], to instead minimize”
On a Link Between Kernel Mean Maps and Fraunhofer Diffraction, with an Application to Super-Resolution Beyond the Diffraction Limit (2013, methodology): “Given a pd kernel k, we define the kernel mean map of X by [24, 28]”
Sharp analysis of low-rank kernel matrix approximations (2012, positive): “First, using the representer theorem, the unique solution f may be found as f = P =1 α i φ ( x i ) (see, e.g., Wahba, 1990; Sch¨olkopf and Smola, 2002; Shawe-Taylor and Cristianini, 2004).”
Detecting low-complexity unobserved causes (2011, background): “The inner product is defined [Schölkopf and Smola, 2002] via 〈k(.”
Kernel Belief Propagation (2011, background): “This extends earlier work of Song et al. (2010) on inference for trees to the case of graphs with loops.”
Generative and Latent Mean Map Kernels (2010, background): “SVMs using nonlinear kernels such as the polynomial and Gaussian kernels have performed strongly for a variety of non-sequential data classification tasks [18].”
Deep architectures and deep learning in chemoinformatics: the prediction of aqueous solubility for drug-like molecules (2013, methodology): “Shallow machine learning methods, such as shallow neural networks or kernel methods, 1 have been applied to chemoinformatics problems with some success, for instance for the prediction of the physical, chemical, or biological properties of molecules 2-5 or the outcome of chemical reactions.”