Sharp Thresholds for High-Dimensional and Noisy Sparsity Recovery Using $\ell _{1}$ -Constrained Quadratic Programming (Lasso)

By Martin J. Wainwright. 2009

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Subfields: Computational Mechanics, Statistics and Probability, Signal Processing

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Citations in the corpus

Best Subset Selection via a Modern Optimization Lens (2015, background): “…Candès and Plan (2009), Donoho (2006), Efron et al. (2004), Greenshtein and Ritov (2004), Knight and Fu (2000), Meinshausen and Bühlmann (2006), Wainwright (2009), Zhang and Huang (2008), Zhao and Yu (2006)] in terms of algorithms and understanding of its theoretical properties; see also the…”
CAM: Causal Additive Models, high-dimensional order search and penalized regression (2013, background): “The former is a well-understood subject thanks to the broad literature in sparse regression and related techniques (Tibshirani, 1996; Meinshausen and Bühlmann, 2006; Yuan and Lin, 2006; Zhao and Yu, 2006; Zou, 2006; Wainwright, 2009, cf.).”
Distributed Multi-Task Learning (2015, background): “Under the irrepresentable condition on the design (which is weaker than the mutual incoherence), the lasso requires the signal to satisfy [Bunea, 2008; Wainwright, 2009]: for some constant C γ,κ of the mutual coherence parameter γ and of κ .”
Stability selection (2008, background): “Substantial understanding has been gained over the last few years about consistency of such lasso variable selection (Meinshausen and Bühlmann, 2006; Zhao and Yu, 2006; Wainwright, 2009; Yuan and Lin, 2007), and we present the details in Section 3.1.”
Robust Lasso With Missing and Grossly Corrupted Observations (2011, methodology): “This behavior is captured similarly by the standard Lasso, as pointed out in the discussion after Corollary 2 of [8].”
High-dimensional Ising model selection using ℓ1-regularized logistic regression (2010, background): “The Annals of Statistics 2010, Vol. 38, No. 3, 1287–1319 DOI: 10.1214/09-AOS691 © Institute of Mathematical Statistics, 2010 HIGH-DIMENSIONAL ISING MODEL SELECTION USING 1-REGULARIZED LOGISTIC REGRESSION”
On the conditions used to prove oracle results for the Lasso (2009, background): “Furthermore, variable selection properties of the Lasso have been studied by [15, 23, 14, 22] and [ 20 ].”
Finding and Leveraging Structure in Learning Problems (2012, methodology): “A straightforward adaptation of results on the LASSO [198] suggest that if the non-zero entries are spread out (say at random) then we would require μ Õ ( σ √ n1n2 m ) for localization.”
On constrained and regularized high-dimensional regression (2013, background): “For L 1 -regularization, Tibshirani (1996), Meinshausen and Buhlmann (2006), Zhao and Yu (2006) and Wainwright (2009) proved that the Lasso is sign consistent and thus selection consistent, under a strong irrepresentable assumption that is nearly necessary.”
Latent variable graphical model selection via convex optimization (2010, methodology): “usual Lasso irrepresentability conditions [32, 37], which are typically imposed on the covariance matrix.”
Selective Sequential Model Selection (2015, neutral): “Much recent model-selection literature focuses on characterizing the regime in which sparsistency is possible; see, e.g. Bickel et al. (2009), Meinshausen and Bühlmann (2006), Negahban et al. (2009), Van De Geer et al. (2009), Wainwright (2009), Zhao and Yu (2006).”