Efficient SVM Training Using Low-Rank Kernel Representations

By Shai Fine, Katya Scheinberg. 2002

717 citations recorded by the source corpus.

Subfields: Optimization & Training, Statistical Learning Theory

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “See Fukumizu et al. (2008; Section 2.2 and 2.3) for a rigorous treatment of this measure. Zhang et al. (2011) resorts to the characterization based on the concept of partial association of Daudin (1980) which says that X ⊥⊥ Y |Z if and only if E[fg] = 0 for all suitable f chosen to be a function fro”
FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test (2014, background): “Many efforts have been made to speedup the establishment of the kernel information and accelerate the implementation of kernel techniques (Smola & Schölkopf, 2000; Williams & Seeger, 2000; Fine & K.Scheinberg, 2001; Si et al., 2014).”
Kernel Bayes' Rule (2010, methodology): “Substantial cost reductions can be a chieved by low rank matrix approximations such as the incomplete Cholesky decomposition [5], which ap proximates a Gram matrix in the form of ΓΓ with n× r matrixΓ.”
A Kernel Method for the Two-Sample-Problem (2006, methodology): “A generalisation of the Wald-Wolfowitz runs test to the multivariate domain was proposed and analysed by Friedman and Rafsky (1979); Henze and Penrose (1999) (FR Wolf), and involves counting the number of edges in the minimum spanning tree over the aggregated data that connect points in X to points ”
Scalable Kernel Methods via Doubly Stochastic Gradients (2014, methodology): “Many work followed this strategy, including Greedy basis selection techniques [1], Nystr¨om approximation [2] and incomplete Cholesky decomposition [3].”
Bayesian Gaussian process models : PAC-Bayesian generalisation error bounds and sparse approximations (2003, methodology): “Although this technique is routinely used in numerical programming, we have come across it via [54].”
Group Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations (2017, neutral): “Typically, each RKHS’s mapping is approximated by performing a projection onto a subspace of ﬁnite dimension, which is a classical approach to make kernel methods work at large scale (Fine and Scheinberg, 2001; Smola and Sch¨olkopf, 2000; Williams and Seeger, 2001).”
Optimization for machine learning (2010, background): “The early attempts to apply IPMs in the support vector machine training context (Ferris and Munson, 2003; Fine and Scheinberg, 2002; Goldfarb and Scheinberg, 2004) were very successful and generated further interest from the optimization community stimulating several new developments (Gertz and Grif”
A New Approach to Collaborative Filtering: Operator Estimation with Spectral Regularization (2008, methodology): “, where X ∈ RN×mX and Y ∈ RN×mY are any square roots, for example, obtained by kernel PCA or incomplete Cholesky decomposition (Fine and Scheinberg, 2001; Bach and Jordan, 2005).”
Kernel Measures of Conditional Dependence (2007, methodology): “With the incomplete Cholesky decomposition [17] of rank r, the complexity to compute Î n is O(r (2)n).”