High-dimensional regression with unknown variance
TLDR
In this paper, a review of recent results for high-dimensional sparse linear regression in the practical case of unknown variance is presented, including coordinate sparsity, group sparsity and variation sparsity.Abstract:
We review recent results for high-dimensional sparse linear re- gression in the practical case of unknown variance. Different sparsity settings are covered, including coordinate-sparsity, group-sparsity and variation- sparsity. The emphasis is put on nonasymptotic analyses and feasible pro- cedures. In addition, a small numerical study compares the practical perfor- mance of three schemes for tuning the lasso estimator and some references are collected for some more general models, including multivariate regres- sion and nonparametric regression.read more
Citations
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Journal ArticleDOI
Robust subspace clustering
TL;DR: This paper introduces an algorithm inspired by sparse subspace clustering (SSC) to cluster noisy data, and develops some novel theory demonstrating its correctness.
Journal ArticleDOI
Robust subspace clustering
TL;DR: In this paper, an algorithm inspired by sparse subspace clustering (SSC) was proposed to cluster noisy data, and a theory demonstrating its correctness was developed by using geometric functional analysis.
Journal ArticleDOI
Non-negative least squares for high-dimensional linear models: Consistency and sparse recovery without regularization
Martin Slawski,Matthias Hein +1 more
TL;DR: In this article, non-negativity constraints on the regression coefficients are used to improve the performance of non-negative least squares (NNLS) for high-dimensional linear models.
ReportDOI
Pivotal estimation via square-root Lasso in nonparametric regression
TL;DR: A self-tuning Lasso method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity and (drastic) non-Gaussianity of the noise, and generates sharp bounds even in extreme cases, such as the infinite variance case and the noiseless case.
Journal ArticleDOI
Pivotal estimation via square-root Lasso in nonparametric regression
TL;DR: A self-tuning Lasso method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity and (drastic) non-Gaussianity of the noise, and generates sharp bounds even in extreme cases, such as the infinite variance case and the noiseless case.
References
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Journal ArticleDOI
Regression Shrinkage and Selection via the Lasso
TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
Journal ArticleDOI
Estimating the Dimension of a Model
TL;DR: In this paper, the problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion.
Book
The Elements of Statistical Learning: Data Mining, Inference, and Prediction
TL;DR: In this paper, the authors describe the important ideas in these areas in a common conceptual framework, and the emphasis is on concepts rather than mathematics, with a liberal use of color graphics.
Book
Compressed sensing
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
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