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Recent extensive numerical experiments in high scale machine learning have allowed to uncover a quite counterintuitive phase transition, as a function of the ratio between the sample size and the number of parameters in the model.
An inverse function theorem via continuous newton’s method
Alfonso Castro and JW Neuberger · 2001
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The continuous newton’s method, inverse functions, and nash-moser
John W Neuberger · 2007
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Near-ideal model selection by ℓ 1 \ell_{1} minimization
Emmanuel J Candès, Yaniv Plan, et al · 2009
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Introduction to the non-asymptotic analysis of random matrices
Roman Vershynin · 2010
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To understand deep learning we need to understand kernel learning
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Trevor Hastie, Andrea Montanari, Saharon Rosset, and Ryan J Tibshirani · 2019
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Benign overfitting in the large deviation regime
Geoffrey Chinot and Matthieu Lerasle · 2020
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Benign overfitting in ridge regression
Alexander Tsigler and Peter L Bartlett · 2020
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Benign overfitting without linearity: Neural network classifiers trained by gradient descent for noisy linear data
Spencer Frei, Niladri S Chatterji, and Peter Bartlett · 2022
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Guillaume Lecué and Zong Shang · 2022
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The generalization error of random features regression: Precise asymptotics and the double descent curve
Song Mei and Andrea Montanari · 2022
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Benign overfitting in linear regression
Peter L Bartlett, Philip M Long, Gábor Lugosi, and Alexander Tsigler · 2020
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High dimensional statistics
Phillippe Rigollet and Jan-Christian Hütter
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