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We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional and non-Gaussian setting.
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Do semidefinite relaxations solve sparse pca up to the information limit?
Robert Krauthgamer, Boaz Nadler, Dan Vilenchik, et al · 2015
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Minimax rate of convergence and the performance of empirical risk minimization in phase retrieval
Guillaume Lecué and Shahar Mendelson · 2015
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On consistency and sparsity for sliced inverse regression in high dimensions
Q. Lin, Z. Zhao, and J. S. Liu · 2015
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Regularized m-estimators with nonconvexity: Statistical and algorithmic theory for local optima
Po-Ling Loh and Martin J Wainwright · 2015
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High dimensional single index models
Peter Radchenko · 2015
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Variable selection for general index models via sliced inverse regression
B. Jiang and J. S. Liu · 2014
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Tighten after relax: Minimax-optimal sparse pca in polynomial time
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Christos Thrampoulidis, Ehsan Abbasi, and Babak Hassibi · 2015
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Phase recovery, maxcut and complex semidefinite programming
Irène Waldspurger, Alexandre d’Aspremont, and Stéphane Mallat · 2015
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Sparse nonlinear regression: Parameter estimation and asymptotic inference
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Non-convex projected gradient descent for generalized low-rank tensor regression
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A shrinkage principle for heavy-tailed data: High-dimensional robust low-rank matrix recovery
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Structured signal recovery from non-linear and heavy-tailed measurements
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Sub-gaussian estimators of the mean of a random matrix with heavy-tailed entries
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Agnostic estimation for misspecified phase retrieval models
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The generalized lasso with non-linear observations
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A geometric analysis of phase retrieval
Ju Sun, Qing Qu, and John Wright · 2016
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Statistical and computational trade-offs in estimation of sparse principal components
Tengyao Wang, Quentin Berthet, Richard J Samworth, et al · 2016
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On the optimality of sliced inverse regression in high dimensions
Qian Lin, Xinran Li, Dongming Huang, and Jun S Liu · 2017
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