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An evolving line of machine learning works observe empirical evidence that suggests interpolating estimators -- the ones that achieve zero training error -- may not necessarily be harmful.
Surprises in high-dimensional ridgeless least squares interpolation
Hastie, T., Montanari, A., Rosset, S., and Tibshirani, R. J. (2019) · 1903
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Mitra, P. P. (2019) · 1906
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Bellec, P. C. and Zhang, C.-H. (2019) · 1912
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Deep double descent: Where bigger models and more data hurt
Nakkiran, P., Kaplun, G., Bansal, Y., Yang, T., Barak, B., and Sutskever, I. (2019) · 1912
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A remark on Stirling’s formula
Robbins, H. (1955) · 1955
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Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · 1996
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Atomic decomposition by basis pursuit
Chen, S. S., Donoho, D. L., and Saunders, M. A. (2001) · 2001
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The elements of statistical learning
Friedman, J., Hastie, T., Tibshirani, R., et al. (2001) · 2001
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Overfitting can be harmless for basis pursuit, but only to a degree
Ju, P., Lin, X., and Liu, J. (2020) · 2002
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A precise high-dimensional asymptotic theory for boosting and min-l1-norm interpolated classifiers
Liang, T. and Sur, P. (2020) · 2002
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Optimal regularization can mitigate double descent
Nakkiran, P., Venkat, P., Kakade, S., and Ma, T. (2020) · 2003
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Boosting as a regularized path to a maximum margin classifier
Rosset, S., Zhu, J., and Hastie, T. (2004) · 2004
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Condition numbers of gaussian random matrices
Chen, Z. and Dongarra, J. J. (2005) · 2005
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Stable recovery of sparse overcomplete representations in the presence of noise
Donoho, D. L., Elad, M., and Temlyakov, V. N. (2005) · 2005
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Near-optimal signal recovery from random projections: Universal encoding strategies?
Candes, E. J. and Tao, T. (2006) · 2006
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Triple descent and the two kinds of overfitting: Where & why do they appear?
d’Ascoli, S., Sagun, L., and Biroli, G. (2020) · 2006
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Compressed sensing
Donoho, D. L. (2006) · 2006
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The Lasso with general Gaussian designs with applications to hypothesis testing
Celentano, M., Montanari, A., and Wei, Y. (2020) · 2007
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Multiple descent: Design your own generalization curve
Chen, L., Min, Y., Belkin, M., and Karbasi, A. (2020) · 2008
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Simultaneous analysis of Lasso and Dantzig selector
Bickel, P. J., Ritov, Y., and Tsybakov, A. B. (2009) · 2009
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Counting faces of randomly projected polytopes when the projection radically lowers dimension
Donoho, D. and Tanner, J. (2009) · 2009
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Message-passing algorithms for compressed sensing
Donoho, D. L., Maleki, A., and Montanari, A. (2009) · 2009
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Sharp thresholds for high-dimensional and noisy sparsity recovery using ℓ 1 \ell_{1} -constrained quadratic programming (lasso)
Wainwright, M. J. (2009) · 2009
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Spectral analysis of large dimensional random matrices
Bai, Z. and Silverstein, J. W. (2010) · 2010
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Message passing algorithms for compressed sensing: II. Analysis and validation
Donoho, D. L., Maleki, A., and Montanari, A. (2010) · 2010
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Stability and instance optimality for gaussian measurements in compressed sensing
Wojtaszczyk, P. (2010) · 2010
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Statistics for high-dimensional data: methods, theory and applications
Bühlmann, P. and van de Geer, S. (2011) · 2011
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Generalized approximate message passing for estimation with random linear mixing
Rangan, S. (2011) · 2011
Cited alongside, same era.
On the robustness of minimum-norm interpolators
Chinot, G., Löffler, M., and van de Geer, S. (2020) · 2012
Cited alongside, same era.
Iterative estimation of constrained rank-one matrices in noise
Rangan, S. and Fletcher, A. K. (2012) · 2012
Cited alongside, same era.
El Karoui, N. (2013) · 2013
Cited alongside, same era.
On robust regression with high-dimensional predictors
El Karoui, N., Bean, D., Bickel, P. J., Lim, C., and Yu, B. (2013) · 2013
Cited alongside, same era.
Precise error analysis of regularized m m -estimators in high dimensions
Thrampoulidis, C., Abbasi, E., and Hassibi, B. (2018) · 2018
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Optimal errors and phase transitions in high-dimensional generalized linear models
Barbier, J., Krzakala, F., Macris, N., Miolane, L., and Zdeborová, L. (2019) · 2019
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Reconciling modern machine-learning practice and the classical bias–variance trade-off
Belkin, M., Hsu, D., Ma, S., and Mandal, S. (2019) · 2019
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The generalization error of random features regression: Precise asymptotics and the double descent curve
Mei, S. and Montanari, A. (2019) · 2019
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A modern maximum-likelihood theory for high-dimensional logistic regression
Sur, P. and Candès, E. J. (2019) · 2019
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State evolution for general approximate message passing algorithms, with applications to spatial coupling
Javanmard, A. and Montanari, A. (2013) · 2013
Cited alongside, same era.
The squared-error of generalized Lasso: A precise analysis
Oymak, S., Thrampoulidis, C., and Hassibi, B. (2013) · 2013
Cited alongside, same era.
A framework to characterize performance of LASSO algorithms
Stojnic, M. (2013) · 2013
Cited alongside, same era.
Living on the edge: Phase transitions in convex programs with random data
Amelunxen, D., Lotz, M., McCoy, M. B., and Tropp, J. A. (2014) · 2014
Cited alongside, same era.
In search of the real inductive bias: On the role of implicit regularization in deep learning
Neyshabur, B., Tomioka, R., and Srebro, N. (2014) · 2014
Cited alongside, same era.
Universality in polytope phase transitions and message passing algorithms
Bayati, M., Lelarge, M., and Montanari, A. (2015) · 2015
Cited alongside, same era.
Asymptotic mutual information for the two-groups stochastic block model
Deshpande, Y., Abbe, E., and Montanari, A. (2015) · 2015
Cited alongside, same era.
The likelihood ratio test in high-dimensional logistic regression is asymptotically a rescaled chi-square
Sur, P., Chen, Y., and Candès, E. J. (2019) · 2019
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Benefits and limitations of genome-wide association studies
Tam, V., Patel, N., Turcotte, M., Bossé, Y., Paré, G., and Meyre, D. (2019) · 2019
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Open problem: Monotonicity of learning
Viering, T., Mey, A., and Loog, M. (2019) · 2019
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Early stopping for kernel boosting algorithms: A general analysis with localized complexities
Wei, Y., Yang, F., and Wainwright, M. J. (2019) · 2019
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The neural tangent kernel in high dimensions: Triple descent and a multi-scale theory of generalization
Adlam, B. and Pennington, J. (2020) · 2020
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Benign overfitting in linear regression
Bartlett, P. L., Long, P. M., Lugosi, G., and Tsigler, A. (2020) · 2020
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Two models of double descent for weak features
Belkin, M., Hsu, D., and Xu, J. (2020) · 2020
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Algorithmic analysis and statistical estimation of SLOPE via approximate message passing
Bu, Z., Klusowski, J. M., Rush, C., and Su, W. J. (2020) · 2020
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Approximate message passing algorithms for rotationally invariant matrices
Fan, Z. (2020) · 2020
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Just interpolate: Kernel “ridgeless” regression can generalize
Liang, T. and Rakhlin, A. (2020) · 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) · 2020
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Harmless interpolation of noisy data in regression
Muthukumar, V., Vodrahalli, K., Subramanian, V., and Sahai, A. (2020) · 2020
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Deep learning: a statistical viewpoint
Bartlett, P. L., Montanari, A., and Rakhlin, A. (2021) · 2021
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Belkin, M. (2021) · 2021
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Local convexity of the TAP free energy and AMP convergence for Z2-synchronization
Celentano, M., Fan, Z., and Mei, S. (2021) · 2021
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Universality of approximate message passing algorithms
Chen, W.-K. and Lam, W.-K. (2021) · 2021
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A unifying tutorial on approximate message passing
Feng, O. Y., Venkataramanan, R., Rush, C., and Samworth, R. J. (2021) · 2021
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Estimation of low-rank matrices via approximate message passing
Montanari, A. and Venkataramanan, R. (2021) · 2021
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Uniform consistency of cross-validation estimators for high-dimensional ridge regression
Patil, P., Wei, Y., Rinaldo, A., and Tibshirani, R. (2021) · 2021
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Understanding deep learning (still) requires rethinking generalization
Zhang, C., Bengio, S., Hardt, M., Recht, B., and Vinyals, O. (2021) · 2021
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Zhong, X., Wang, T., and Fan, Z. (2021) · 2021
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