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Single-Index Models are high-dimensional regression problems with planted structure, whereby labels depend on an unknown one-dimensional projection of the input via a generic, non-linear, and potentially non-deterministic transformation.
Generalized Linear Models
P. McCullagh and J.A. Nelder · 1983
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Semiparametric least squares (sls) and weighted sls estimation of single-index models
Hidehiko Ichimura · 1993
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Efficient noise-tolerant learning from statistical queries
Michael Kearns · 1998
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Direct estimation of the index coefficient in a single-index model
Marian Hristache, Anatoli Juditsky, and Vladimir Spokoiny · 2001
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Wolfgang Härdle, Marlene Müller, Stefan Sperlich, and Axel Werwatz · 2004
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Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
Jinho Baik, Gérard Ben Arous, and Sandrine Péché · 2005
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Methods of Numerical Integration
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A new algorithm for estimating the effective dimension-reduction subspace
Arnak S Dalalyan, Anatoly Juditsky, and Vladimir Spokoiny · 2008
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The isotron algorithm: High-dimensional isotonic regression
Adam Tauman Kalai and Ravi Sastry · 2009
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Efficient learning of generalized linear and single index models with isotonic regression
Sham M Kakade, Varun Kanade, Ohad Shamir, and Adam Kalai · 2011
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Jelani Nelson, Huy Nguyen, and David P. Woodruff · 2012
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A statistical model for tensor pca, 2014
Andrea Montanari and Emile Richard · 2014
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Fast spectral algorithms from sum-of-squares proofs: tensor decomposition and planted sparse vectors
Samuel B Hopkins, Tselil Schramm, Jonathan Shi, and David Steurer · 2016
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Correspondence retrieval
Alexandr Andoni, Daniel Hsu, Kevin Shi, and Xiaorui Sun · 2017
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Sum-of-squares certificates for maxima of random tensors on the sphere, 2017
Vijay Bhattiprolu, Venkatesan Guruswami, and Euiwoong Lee · 2017
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Statistical query lower bounds for robust estimation of high-dimensional gaussians and gaussian mixtures
Ilias Diakonikolas, Daniel M Kane, and Alistair Stewart · 2017
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Statistical algorithms and a lower bound for detecting planted cliques
Vitaly Feldman, Elena Grigorescu, Lev Reyzin, Santosh S. Vempala, and Ying Xiao · 2017
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Learning single-index models in gaussian space
Rishabh Dudeja and Daniel Hsu · 2018
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Samuel Hopkins · 2018
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Marco Mondelli and Andrea Montanari · 2018
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Amelia Perry, Alexander S Wein, Afonso S Bandeira, and Ankur Moitra · 2018
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Optimal errors and phase transitions in high-dimensional generalized linear models
Jean Barbier, Florent Krzakala, Nicolas Macris, Léo Miolane, and Lenka Zdeborová · 2019
Emmanuel Abbe, Enric Boix-Adsera, and Theodor Misiakiewicz · 2022
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Learning single-index models with shallow neural networks
Alberto Bietti, Joan Bruna, Clayton Sanford, and Min Jae Song · 2022
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The franz-parisi criterion and computational trade-offs in high dimensional statistics
Afonso S Bandeira, Ahmed El Alaoui, Samuel Hopkins, Tselil Schramm, Alexander S Wein, and Ilias Zadik · 2022
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Non-gaussian component analysis via lattice basis reduction
Ilias Diakonikolas and Daniel Kane · 2022
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Neural networks can learn representations with gradient descent
Alexandru Damian, Jason Lee, and Mahdi Soltanolkotabi · 2022
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Sharp recovery thresholds of tensor pca spectral algorithms
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Average-case complexity of tensor decomposition for low-degree polynomials
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Statistical-computational trade-offs in tensor pca and related problems via communication complexity, 2024
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