On Relevant Dimensions in Kernel Feature Spaces

By Mikio L. Braun, Joachim M. Buhmann, K. Müller. 2008

138 citations recorded by the source corpus.

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

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Citations in the corpus

Security analysis of online centroid anomaly detection (2010, background): “By pruning the eigenvalues “responsible” for dimensions with low variance one can reduce the size of the feature space to the implicit dimensionality of the problem if the kernel matches the data (Braun et al., 2008).”
Explaining nonlinear classification decisions with deep Taylor decomposition (2015, methodology): “Some methods seek to provide a global understanding of the trained model, by measuring important characteristics of it, such as the noise and relevant dimensionality of its feature space(s) [28, 29, 30], its invariance to certain”
Evaluating the Visualization of What a Deep Neural Network Has Learned (2015, background): “Note that this aspect differs from feature selection [12], where the question is: which features are on average salient for the ensemble of training data? Only recently, the transparency problem has been receiving more attention for general nonlinear estimators [13]–[16].”
Understanding Machine-learned Density Functionals (2014, background): “A good choice of kernel can reflect the characteristics of the data (see [52]).”
Exploring chemical compound space with quantum-based machine learning (2019, background): “This result hints on the potential sparsity of CCS, implying a low complexity and dimensionality [89] of the property prediction problem throughout CCS.”
A Unifying Review of Deep and Shallow Anomaly Detection (2020, methodology): “For shallow methods, the problem is well studied, and we have many effective methods [5], [259], [326], [372], [374], [375], [471].”
Fast cross-validation via sequential testing (2012, result): “Chien et al. (1995, 1999) devise a similar range of algorithms using concepts of PAC learning and game theory: Different hypotheses are ordered by their expected utility according to the test data the algorithm has seen so far. As for Hoeffding Races, the emphasis in this approach lies on reducing t”
Layer-Wise Relevance Propagation for Deep Neural Network Architectures (2016, background): “Several works have been dedicated to the understanding of general non-linear estimators [4, 3, 12].”
On layer-wise representations in deep neural networks (2013, methodology): “An important aspect of the noise and dimensionality estimates proposed by Braun et al. (2008) is the advantageous convergence property of the signal component S(i) with respect to the infinite sample case.”
Kernel Analysis of Deep Networks (2011, methodology): “KERNEL ANALYSIS OF DEEP NETWORKS y x dimensionality of the problem noise bed i |u T i Y | Figure 8: Illustration of the concept of relevant dimensions in kernel feature spaces (Braun et al., 2008 ).”
Machine learning for molecular simulation (2019, background): “As DTNNs are end-to-end trained to predict certain quantum mechanical quantities, such as potential energies, they learn the representation that is relevant for the task of predicting these quantities [111].”
Introduction to machine learning for brain imaging (2011, background): “Note that recently Braun et al. (2008) has observed that the excellent generalization that is typically observed when using SVMs in high dimensional applications with few samples is due to its very economic representation in Kernel Hilbert space.”