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We present a novel view on principal component analysis (PCA) as a competitive game in which each approximate eigenvector is controlled by a player whose goal is to maximize their own utility function.
The method of stochastic approximation for the determination of the least eigenvalue of a symmetrical matrix
TP Krasulina · 1969
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Simultaneous iteration method for symmetric matrices
H Rutishauser · 1971
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Simplified neuron model as a principal component analyzer
Erkki Oja · 1982
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Nash and correlated equilibria: some complexity considerations
Itzhak Gilboa and Eitan Zemel · 1989
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Anthony J Bell and Terrence J Sejnowski · 1997
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Eigenvalue computation in the 20th century
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The Organization of Behavior: A Neuropsychological Theory
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Optimization Algorithms on Matrix Manifolds
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The complexity of computing a Nash equilibrium
Constantinos Daskalakis, Paul W Goldberg, and Christos H Papadimitriou · 2009
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Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions
Nathan Halko, Per-Gunnar Martinsson, and Joel A Tropp · 2011
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Matrix Computations , volume 3
Gene H Golub and Charles F Van Loan · 2012
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Matrix Analysis
Roger A Horn and Charles R Johnson · 2012
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Guillaume Desjardins, Karen Simonyan, Razvan Pascanu, et al · 2015
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Xi Chen, Yan Duan, Rein Houthooft, John Schulman, Ilya Sutskever, and Pieter Abbeel · 2016
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Preserving privacy between features in distributed estimation
Christina Heinze-Deml, Brian McWilliams, and Nicolai Meinshausen · 2018
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Disentangling disentanglement in variational autoencoders
Emile Mathieu, Tom Rainforth, N Siddharth, and Yee Whye Teh · 2018
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Spectral normalization for generative adversarial networks
Takeru Miyato, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida · 2018
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Lipschitz regularity of deep neural networks: analysis and efficient estimation
Aladin Virmaux and Kevin Scaman · 2018
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An implicit form of Krasulina’s k-PCA update without the orthonormality constraint
Ehsan Amid and Manfred K Warmuth · 2019
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Mina Ghashami, Edo Liberty, Jeff M Phillips, and David P Woodruff · 2016
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Christina Heinze, Brian McWilliams, and Nicolai Meinshausen · 2016
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Gabriel Krummenacher, Brian McWilliams, Yannic Kilcher, Joachim M Buhmann, and Nicolai Meinshausen · 2016
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First efficient convergence for streaming k-PCA: a global, gap-free, and near-optimal rate
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Input sparsity time low-rank approximation via ridge leverage score sampling
Michael B Cohen, Cameron Musco, and Christopher Musco · 2017
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Global rates of convergence for nonconvex optimization on manifolds
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Fast and communication-efficient distributed pca
Arpita Gang, Haroon Raja, and Waheed U Bajwa · 2019
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Eigenvalue and generalized eigenvalue problems: Tutorial
Benyamin Ghojogh, Fakhri Karray, and Mark Crowley · 2019
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Challenging common assumptions in the unsupervised learning of disentangled representations
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Learning interpretable disentangled representations using adversarial VAEs
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Exponentially convergent stochastic k-PCA without variance reduction
Cheng Tang · 2019
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Turning big data into tiny data: Constant-size coresets for k-means, PCA, and projective clustering
Dan Feldman, Melanie Schmidt, and Christian Sohler · 2020
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Distributed stochastic algorithms for high-rate streaming principal component analysis
Haroon Raja and Waheed U Bajwa · 2020
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