Learning the Kernel with Hyperkernels

By Cheng Soon Ong, Alex Smola, Robert C. Williamson. Journal of machine learning research, 2005

372 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/1889b9c3e8bc1118448b95fca38d6eff0bfca64d

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Citations in the corpus

Predicting abnormal returns from news using text classification (2008, methodology): “…probability in (1) by learning an optimal linear combination of kernels (Bousquet and Herrmann 2003, Bach et al. 2004, Lanckriet et al. 2004a, Ong et al. 2005, Sonnenberg et al. 2006, Micchelli and Pontil 2007, Zien and Ong 2007, Rakotomamonjy et al. 2008, Gönen and Alpaydin 2011).”
L2 Regularization for Learning Kernels (2009, background): “Some of this previous work examines families of Gaussian kernels (Micchelli & Pontil, 2005) or hyperkernels (Ong et al., 2005).”
A multiple-kernel support vector regression approach for stock market price forecasting (2011, methodology): “Multiple-kernel learning based on hyperkernels has also been studied (Ong et al., 2005; Tsang & Kwok, 2006).”
Simple and Efficient Multiple Kernel Learning by Group Lasso (2010, methodology): “We compare MKLGL with several state-of-the-art efficient MKL algorithms including: Semi-infinite Programming (SIP) (Kloft et al., 2009; Sonnenburg et al., 2006), the subgradient descent approach used in the SimpleMKL toolbox (Rakotomamonjy et al., 2008), and the level method (Xu et al., 2009a).”
Learning Bounds for Support Vector Machines with Learned Kernels (2006, background): “Infinite-dimensional kernel families have also been considered, either through hyperkernels [11] or as convex combinations of a continuum of base kernels (e.”
Nonmyopic active learning of Gaussian processes: an exploration-exploitation approach (2007, background): “There is also a large body of work on kernel learning (c.f., Ong et al. (2005)).”
Universal Kernels (2006, background): “For recent work in this direction, see Argyriou et al. (2005, 2006), Bach et al. (2004), Lanckriet et al. (2004), Micchelli and Pontil (2005), Micchelli et al. (2006), Neumann et al. (2004), Ong et al. (2005), Sonnenburg et al. (2006) and references therein.”
Learning The Discriminative Power-Invariance Trade-Off (2007, background): “There are many ways of converting distances to inner products and one is free to choose whichever embedding is most suitable.”
A Binary Classification Framework for Two-Stage Multiple Kernel Learning (2012, methodology): “The approach proposed in this paper can also be cast in the framework of learning with hyperkernels (Ong et al., 2005) which provides a general recipe for kernel learning and includes Multiple Kernel Learning”
Generalization bounds for learning the kernel (2009, methodology): “Similar problems studied recently include the so-called COSSO estimate for additive model [18], hyperkernels [22], Bayesian probabilistic kernel learning models [14], and kernel discriminant analysis [30] etc.”
Hyperparameter Learning for Graph Based Semi-supervised Learning Algorithms (2006, background): “(Ong et al., 2005; Ong & Smola, 2003) proposed an interesting measure of kernel space capacity called hyperkernels.”
More generality in efficient multiple kernel learning (2009, methodology): “Other interesting approaches have been proposed in (Argyriou et al., 2005; Ong et al., 2005; Zien & Ong, 2007) and include Hy-perkernels and multi-class MKL. Note that these methods essentially learn linear combinations of base kernels subject to l 1 , or sometimes l 2 (Cristianini et al., 2001;…”
Multiclass multiple kernel learning (2007, background): “Relation to Previous Work There have been several developments on optimizing a linear combination of kernels while training a predictor [1, 3, 6, 8, 12, 14, 15, 20] ([16, 18] considers general parameterized kernel functions).”
l p -Norm Multiple Kernel Learning (2011, background): “Alternatively, E could be obtained by computing pairwise kernel alignments Eij = <Ki,Kj> ‖Ki‖ ‖Kj‖ given a dot product on the space of kernels such as the Frobenius dot product (Ong et al., 2005).”