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The Column Subset Selection Problem (CSSP) and the Nystr\"om method are among the leading tools for constructing small low-rank approximations of large datasets in machine learning and scientific computing.
Two models of double descent for weak features
Belkin, M., Hsu, D., and Xu, J · 1903
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Inequalities
Hardy, G., Littlewood, J., and Pólya, G · 1952
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The coincidence approach to stochastic point processes
Macchi, O · 1975
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Some applications of the rank revealing QR factorization
Chan, T. F. and Hansen, P. C · 1992
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Efficient algorithms for computing a strong rank-revealing qr factorization
Gu, M. and Eisenstat, S. C · 1996
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Gaussian regression and optimal finite dimensional linear models
Santa, H. Z., Zhu, H., Williams, C. K. I., Rohwer, R., and Morciniec, M · 1997
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Kernel independent component analysis
Bach, F. R. and Jordan, M. I · 2003
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An introduction to variable and feature selection
Guyon, I. and Elisseeff, A · 2003
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On the Nyström method for approximating a Gram matrix for improved kernel-based learning
Drineas, P. and Mahoney, M. W · 2005
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Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Chung, F. and Lu, L · 2006
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Matrix approximation and projective clustering via volume sampling
Deshpande, A., Rademacher, L., Vempala, S., and Wang, G · 2006
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Determinantal processes and independence
Hough, J. B., Krishnapur, M., Peres, Y., Virág, B., et al · 2006
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Gaussian Processes for Machine Learning
Rasmussen, C. E. and Williams, C. K. I · 2006
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An improved approximation algorithm for the column subset selection problem
Boutsidis, C., Mahoney, M., and Drineas, P · 2008
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Relative-error CUR matrix decompositions
Drineas, P., Mahoney, M. W., and Muthukrishnan, S · 2008
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Using the Nyström method to speed up kernel machines
Williams, C. K. I. and Seeger, M · 2008
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Spectral methods in machine learning and new strategies for very large datasets
Belabbas, M.-A. and Wolfe, P. J · 2009
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High-dimensional matched subspace detection when data are missing
Balzano, L., Recht, B., and Nowak, R · 2010
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Efficient volume sampling for row/column subset selection
Deshpande, A. and Rademacher, L · 2010
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Near optimal column-based matrix reconstruction
Boutsidis, C., Drineas, P., and Magdon-Ismail, M · 2011
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LIBSVM: A library for support vector machines
Chang, C.-C. and Lin, C.-J · 2011
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k-DPPs: Fixed-Size Determinantal Point Processes
Kulesza, A. and Taskar, B · 2011
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Optimal column-based low-rank matrix reconstruction
Guruswami, V. and Sinop, A. K · 2012
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Determinantal Point Processes for Machine Learning
Kulesza, A. and Taskar, B · 2012
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Approximate computation and implicit regularization for very large-scale data analysis
Mahoney, M. W · 2012
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A determinantal point process for column subset selection
Belhadji, A., Bardenet, R., and Chainais, P · 2018
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Reverse iterative volume sampling for linear regression
Dereziński, M. and Warmuth, M. K · 2018
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Restricted Strong Convexity Implies Weak Submodularity
Elenberg, E. R., Khanna, R., Dimakis, A. G., and Negahban, S · 2018
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Benign overfitting in linear regression
Bartlett, P. L., Long, P. M., Lugosi, G., and Tsigler, A · 2019
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Rates of convergence for sparse variational Gaussian process regression
Burt, D., Rasmussen, C. E., and Van Der Wilk, M · 2019
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Faster subset selection for matrices and applications
Avron, H. and Boutsidis, C · 2013
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Optimal CUR matrix decompositions
Boutsidis, C. and Woodruff, D. P · 2014
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Diverse sequential subset selection for supervised video summarization
Gong, B., Chao, W.-L., Grauman, K., and Sha, F · 2014
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Fast randomized kernel ridge regression with statistical guarantees
Alaoui, A. E. and Mahoney, M. W · 2015
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Column selection via adaptive sampling
Paul, S., Magdon-Ismail, M., and Drineas, P · 2015
Cited alongside, same era.
Greedy column subset selection: New bounds and distributed algorithms
Altschuler, J., Bhaskara, A., Fu, G., Mirrokni, V., Rostamizadeh, A., and Zadimoghaddam, M · 2016
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Fast determinantal point processes via distortion-free intermediate sampling
Dereziński, M · 2019
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Exact sampling of determinantal point processes with sublinear time preprocessing
Dereziński, M., Calandriello, D., and Valko, M · 2019
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DPPy: DPP Sampling with Python
Gautier, G., Polito, G., Bardenet, R., and Valko, M · 2019
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Double descent in the condition number
Poggio, T., Kur, G., and Banburski, A · 2019
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Beyond worst-case analysis
Roughgarden, T · 2019
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Block basis factorization for scalable kernel evaluation
Wang, R., Li, Y., Mahoney, M. W., and Darve, E · 2019
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Tensorized determinantal point processes for recommendation
Warlop, R., Mary, J., and Gartrell, M · 2019
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Sampling from a k k -dpp without looking at all items
Calandriello, D., Dereziński, M., and Valko, M · 2020
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Determinantal point processes in randomized numerical linear algebra
Dereziński, M. and Mahoney, M. W · 2020
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Exact expressions for double descent and implicit regularization via surrogate random design
Dereziński, M., Liang, F., and Mahoney, M. W · 2020
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Bayesian experimental design using regularized determinantal point processes
Dereziński, M., Liang, F., and Mahoney, M · 2020
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On the multiple descent of minimum-norm interpolants and restricted lower isometry of kernels
Liang, T., Rakhlin, A., and Zhai, X · 2020
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Liao, Z., Couillet, R., and Mahoney, M. W · 2020
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Convergence analysis of block coordinate algorithms with determinantal sampling
Mutny, M., Dereziński, M., and Krause, A · 2020
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