Kernel Methods for Pattern Analysis

By John Shawe-Taylor, Nello Cristianini. 2004

7,213 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

Neural Tangent Kernel: Convergence and Generalization in Neural Networks (2018, background): “, f (NnL) of the data with respect to to the kernel K [17, 18].”
Analysis of a Random Forests Model (2010, background): “As highlighted by various empirical studies (see [11, 36, 20, 24, 25] for instance), random forests have emerged as serious competitors to state-of-the-art methods such as boosting (Freund [22]) and support vector machines (Shawe-Taylor and Cristianini [35]).”
Framing Image Description as a Ranking Task: Data, Models and Evaluation Metrics (2013, methodology): “BoW1 is the Bag of Words baseline using 1 caption per training image, BoW5 is with all 5 captions, TagRank [Hwang and Grauman, 2012], TRI5 is the baseline using the subsequence string kernel [Shawe-Taylor and Cristianini, 2004], and TRI5SEM is our final model incorporating lexical semantics.”
Predicting Parameters in Deep Learning (2013, neutral): “Kernel ridge regression is a way to extend standard linear regression to learn non-linear functions by using kernels; see for example [25].”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “Under the assumption that EY |X [g(Y )|X] ∈H , Song et al. (2009) shows that the conditional mean embedding given in Definition 4.”
Security analysis of online centroid anomaly detection (2010, methodology): “Notice that all operations can be carried out using kernel functions – a standard trick known since the kernel PCA (Schölkopf et al., 1998; Shawe-Taylor and Cristianini, 2004) – which substantially increases the discriminative power of this method.”
Taking Advantage of Multitask Learning for Fair Classification (2018, neutral): “[33 34] and references therein.”
Prototypal Analysis and Prototypal Regression (2017, methodology): “Kernel methods and reproducing kernel Hilbert space (RKHS) are widely used in machine learning to extend algorithms where only inner products among data points are required (Schölkopf and Smola, 2002; Shawe-Taylor and Cristianini, 2004; Hofmann et al., 2008).”
Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families (2015, methodology): “In order to allow for large n , and to exploit potential manifold structure in the RKHS, we apply a low-rank approximation to the kernel matrix via incomplete Cholesky [28, Alg.”
Optimal Rates for Random Fourier Features (2015, background): “1 (McDiarmid Inequality [7]).”
Computing functions of random variables via reproducing kernel Hilbert space representations (2015, neutral): “Kernel methods in machine learning, such as Support Vector Machines or Kernel PCA, are based onmapping the data into a reproducing kernel Hilbert space (RKHS)H (Boser et al. 1992; Schölkopf and Smola 2002; Shawe-Taylor and Cristianini 2004; Hofmann et al. 2008; Steinwart and Christmann 2008), Φ : X ”
Kernel Mean Estimation via Spectral Filtering (2014, background): “…in a reproducing kernel Hilbert space (RKHS) computed w.r.t. some distribution P , has played a fundamental role as a basic building block of many kernel-based learning algorithms [2–4], and has recently gained increasing attention through the notion of embedding distributions in an RKHS [5– 13].”
Kernel Mean Shrinkage Estimators (2014, methodology): “Moreover, the kernel mean also served as a basis in early development of algorithms for classiﬁcation, density estimation, and anomaly detection (Shawe-Taylor and Cristianini, 2004, Chapter 5).”
Sharp analysis of low-rank kernel matrix approximations (2012, neutral): “For more details, see, e.g., Rasmussen and Williams (2006); Sch¨olkopf and Smola (2002); Shawe-Taylor and Cristianini (2004).”
Conditional mean embeddings as regressors (2012, methodology): “In particular, a popular method to sparsify is the incomplete Cholesky decomposition (Shawe-Taylor & Cristianini, 2004), which sparsiﬁes based on the distribution on the input space X only.”