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We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under the restricted isometry assumption.
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Frank Bauer, Sergei Pereverzev, and Lorenzo Rosasco · 2007
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Sara van de Geer · 2007
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On early stopping in gradient descent learning
Yuan Yao, Lorenzo Rosasco, and Andrea Caponnetto · 2007
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A simple proof of the restricted isometry property for random matrices
Richard Baraniuk, Mark Davenport, Ronald DeVore, and Michael Wakin · 2008
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Linear convergence of iterative soft-thresholding
Kristian Bredies and Dirk A. Lorenz · 2008
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Majorizing measures and proportional subsets of bounded orthonormal systems
Olivier Guédon, Shahar Mendelson, Alain Pajor, Nicole Tomczak-Jaegermann, et al · 2008
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Fixed-point continuation for ℓ _ 1 \ell\_1 -minimization: Methodology and convergence
Elaine T Hale, Wotao Yin, and Yin Zhang · 2008
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Uniform uncertainty principle for bernoulli and subgaussian ensembles
Shahar Mendelson, Alain Pajor, and Nicole Tomczak-Jaegermann · 2008
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On sparse reconstruction from fourier and gaussian measurements
Mark Rudelson and Roman Vershynin · 2008
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Peter J Bickel, Ya’acov Ritov, Alexandre B Tsybakov, et al · 2009
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Albert Cohen, Wolfgang Dahmen, and Ronald DeVore · 2009
Certifying the restricted isometry property is hard
Afonso S Bandeira, Edgar Dobriban, Dustin G Mixon, and William F Sawin · 2013
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Neal Parikh, Stephen Boyd, et al · 2014
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Early stopping and non-parametric regression: an optimal data-dependent stopping rule
Garvesh Raskutti, Martin J Wainwright, and Bin Yu · 2014
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Lower bounds on the performance of polynomial-time algorithms for sparse linear regression
Yuchen Zhang, Martin J Wainwright, and Michael I Jordan · 2014
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Statistical learning with sparsity: the lasso and generalizations
Robert Tibshirani, Martin Wainwright, and Trevor Hastie · 2015
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Best subset selection via a modern optimization lens
Dimitris Bertsimas, Angela King, and Rahul Mazumder · 2016
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Lasso-type recovery of sparse representations for high-dimensional data
Nicolai Meinshausen and Bin Yu · 2009
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Compressive sensing by random convolution
Justin Romberg · 2009
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On the conditions used to prove oracle results for the lasso
Sara A Van De Geer, Peter Bühlmann, et al · 2009
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Fast global convergence rates of gradient methods for high-dimensional statistical recovery
Alekh Agarwal, Sahand Negahban, and Martin J Wainwright · 2010
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Regularization paths for generalized linear models via coordinate descent
Jerome Friedman, Trevor Hastie, and Rob Tibshirani · 2010
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Restricted eigenvalue properties for correlated gaussian designs
Garvesh Raskutti, Martin J Wainwright, and Bin Yu · 2010
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Local linear convergence of ISTA and FISTA on the LASSO problem
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Understanding deep learning requires rethinking generalization
Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals · 2016
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Implicit regularization in matrix factorization
Suriya Gunasekar, Blake E Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, and Nati Srebro · 2017
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Extended comparisons of best subset selection, forward stepwise selection, and the lasso
Trevor Hastie, Robert Tibshirani, and Ryan J Tibshirani · 2017
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Early stopping for kernel boosting algorithms: A general analysis with localized complexities
Yuting Wei, Fanny Yang, and Martin J Wainwright · 2017
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A continuous-time view of early stopping for least squares regression
Alnur Ali, J Zico Kolter, and Ryan J Tibshirani · 2018
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Algorithmic regularization in over-parameterized matrix sensing and neural networks with quadratic activations
Yuanzhi Li, Tengyu Ma, and Hongyang Zhang · 2018
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Iterate averaging as regularization for stochastic gradient descent
Gergely Neu and Lorenzo Rosasco · 2018
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The implicit bias of gradient descent on separable data
Daniel Soudry, Elad Hoffer, Mor Shpigel Nacson, Suriya Gunasekar, and Nathan Srebro · 2018
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Connecting optimization and regularization paths
Arun Suggala, Adarsh Prasad, and Pradeep K Ravikumar · 2018
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High-dimensional statistics: A non-asymptotic viewpoint , volume 48
Martin J Wainwright · 2019
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Peng Zhao, Yun Yang, and Qiao-Chu He · 2019
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