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Empirical Risk Minimization (ERM) algorithms are widely used in a variety of estimation and prediction tasks in signal-processing and machine learning applications.
On general minimax theorems
Maurice Sion · 1958
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The convolution inequality for entropy powers
N. Blachman · 1965
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Convex analysis
R Tyrell Rockafellar · 1997
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Fisher information inequalities and the central limit theorem
Oliver Johnson and Andrew Barron · 2004
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Variational analysis
R Tyrrell Rockafellar and Roger J-B Wets · 2009
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Various thresholds for ℓ 1 \ell_{1} -optimization in compressed sensing
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The noise-sensitivity phase transition in compressed sensing
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Robust statistics
Peter J Huber · 2011
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The lasso risk for gaussian matrices
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The convex geometry of linear inverse problems
Venkat Chandrasekaran, Benjamin Recht, Pablo A Parrilo, and Alan S Willsky · 2012
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Optimal phase transitions in compressed sensing
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Living on the edge: A geometric theory of phase transitions in convex optimization
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Noureddine El Karoui · 2013
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Samet Oymak, Christos Thrampoulidis, and Babak Hassibi · 2013
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A framework to characterize performance of lasso algorithms
Mihailo Stojnic · 2013
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Mathematics of sparsity (and a few other things)
Emmanuel J Candès · 2014
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Variance breakdown of huber (m)-estimators: n/p \rightarrow m\in (1,\infty)
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Lasso with non-linear measurements is equivalent to one with linear measurements
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Fundamental barriers to high-dimensional regression with convex penalties
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A model of double descent for high-dimensional binary linear classification
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Asymptotics and optimal designs of slope for sparse linear regression
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The replica-symmetric prediction for random linear estimation with gaussian matrices is exact
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The impact of regularization on high-dimensional logistic regression
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A modern maximum-likelihood theory for high-dimensional logistic regression
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Does slope outperform bridge regression?
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