Predictive low-rank decomposition for kernel methods

By Francis R. Bach, Michael I. Jordan. 2005

261 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

Improved Nyström low-rank approximation and error analysis (2008, background): “One future direction is to utilize label/side information for task-speci.c decomposition, where one excellent example is (Bach & Jordan, 2005) in the context of incomplete Cholesky decomposition.”
Nyström Method vs Random Fourier Features: A Theoretical and Empirical Comparison (2012, methodology): “, incomplete Cholesky decomposition [3]) have been used to alleviate the computational challenge of kernel methods, they still require computing the kernel matrix.”
Sampling Methods for the Nyström Method (2012, unknown): “A closely related algorithm, known as the Incomplete Cholesky Decomposition (Fine and Scheinberg, 2002; Bach and Jordan, 2002, 2005), can also be viewed as a specific sampling technique associated with the Nyström method (Bach and Jordan, 2005).”
Regression on Fixed-Rank Positive Semidefinite Matrices: A Riemannian Approach (2010, methodology): “Indeed, whereas algorithms based on full-rank matrices scale as O(d3) and require O(d2) storage units, algorithms based on low-rank matrices scale as O(dr2) and require O(dr) storage units (Fine et al., 2001; Bach and Jordan, 2005).”
Randomized numerical linear algebra: Foundations and algorithms (2020, methodology): “These techniques lead to Nyström approximations with superior learning performance; for example, see (Fine and Scheinberg 2001, Bach and Jordan 2005, Bach 2013).”
Recent Advances of Large-Scale Linear Classification (2012, methodology): “Some examples include Nyström mehtod [73], [74] and incomplete Cholesky factorization [75], [76].”
Generalized RBF feature maps for Efficient Detection (2010, methodology): “An alternative to the method we propose is to employ Nyström-type approximations [1, 3, 22] to obtain linear feature maps, but these require a data dependent training step that we avoid here.”
Revisiting the Nystrom Method for Improved Large-scale Machine Learning (2013, background): “sing include [53, 7, 11, 57, 8, 10, 9]. Much of this work has focused on new proposals for selecting columns (e.g., [69, 67, 42, 1, 41]) and/or coupling the method with downstream applications (e.g., [5, 17, 34, 33, 43, 4]). The most detailed results are provided by [39] (as well as the conference p”
Compact Random Feature Maps (2013, background): “To solve this challenge, several schemes have been proposed to explicitly approximate the kernel matrix, including low-rank approximations (Blum, 2006) (Bach & Jordan, 2005), sampling individual entries (Achliop-tas et al., 2002), or discarding entire rows (Drineas & Mahoney, 2005).”
Building Support Vector Machines with Reduced Classifier Complexity (2006, methodology): “We also tried the method of Bach and Jordan (2005) which uses the training labels, but we noticed little improvement.”
Random Fourier Approximations for Skewed Multiplicative Histogram Kernels (2010, methodology): “In [13, 14], the authors proposed incomplete Cholesky decomposition methods that compute a low-rank approximation to the kernel matrix while simultaneously solving the SVM optimization.”