Classes of Kernels for Machine Learning: A Statistics Perspective

By Marc G. Genton. 2002

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “This leads to a number of kernel functions in various application domains (Genton 2002).”
Kernel Mean Shrinkage Estimators (2014, background): “l. As a result, the property of stationary kernel discussed earlier applies immediately to this class of kernel functions. For more detailed account on diﬀerent classes of kernel functions, see e.g., Genton (2002) and Rasmussen and Williams (2006, Chapter 4). In summary, we have illustrated that mea”
FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test (2014, methodology): “2 Efficient Approximation of MMD The following classical theorem from harmonic analysis pro vides the main fundament underlying our approximation method (Genton, 2001).”
A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning (2010, background): “, [Genton, 2001] or [Rasmussen and Williams, 2006, Chapter 4] for an overview).”
Improving MMD-GAN Training with Repulsive Loss Function (2018, methodology): “Generative adversarial nets (GANs) (Goodfellow et al. (2014)) are a branch of generative models that learns to mimic the real data generating process. GANs have been intensively studied in recent years, with a variety of successful applications (Karras et al. (2018); Li et al. (2017b); Lai et al. (2”
Machine learning: a review of classification and combining techniques (2006, background): “Genton (2001) described several classes of kernels, however, he did not address the question of which class is best suited to a given problem.”
Bayesian reasoning and machine learning (2012, unknown): “We refer the reader to [230] and [107] for further popular covariance functions.”
Outlier Detection (2008, unknown): “For certain stationary kernels [16], e.”
Revisiting the Nystrom Method for Improved Large-scale Machine Learning (2013, background): “nstruct sparse Gaussian RBFK matrices A(˙,,C) ij = 2 4 1 x i xj 2 2 C ! 3 5 + exp x i xj 2 ˙2 , where [x]+=maxf0, xg. When is larger than (d +1)=2, this kernel matrix is positive semideﬁ- nite [27]. Increasing shrinks the magnitudes of the off-diagonal entries of the matrix toward zero. As the cut”
Manifold Regularization for Kernelized LSTD (2017, background): “The kernel k can be selected as a tensor product kernel k(x, x′) = k1(s, s)k2(a, a ′), where x = (s, a) (note that the multiplication of two kernels is a kernel [12]).”
Supervised Machine Learning: A Review of Classification Techniques (2007, unknown): “Genton (2001) described several classes of kernels, however, he did not address the question of which class is best suited to a given problem.”
Spectral bias and task-model alignment explain generalization in kernel regression and infinitely wide neural networks (2020, methodology): “[35] Marc G Genton.”
Bayesian Optimization over Sets (2019, background): “In addition, its structure of kernel is k st ( d ( X (1) , X (2) )) where k st ( · ) is a stationary kernel [12] and d ( , · ) is some distance function over two sets (e.g., in [10] the ﬁrst Wasserstein distance).”
Differentiable Compositional Kernel Learning for Gaussian Processes (2018, background): “Beyond stationary kernels, Generalized Bochner’s Theorem (Yaglom, 2012; Kakihara, 1985; Genton, 2001) presents a spectral representation for a larger class of kernels.”
Support Measure Data Description for group anomaly detection (2015, unknown): “, ‖μPi‖2 = 1 and Stationary kernels[9], which are kernels of the form kI(x,x ′) = f(x− x′), that is, they only depend on the difference x− x′.”