On the LASSO and its Dual

By Michael R. Osborne, Brett Presnell, Berwin A. Turlach. 2000

807 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7aa39f7f3b69473705e247dd2b3a9689f10fbbc3

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Citations in the corpus

The Group-Lasso for generalized linear models: uniqueness of solutions and efficient algorithms (2008, methodology): “In particular, we demonstrate that the proposed completeness test successfully detects ambiguous solutions and thus avoids the misinterpretation of “identiﬁed” explanatory factors.”
Recognizing Actions in 3D Using Action-Snippets and Activated Simplices (2016, methodology): “In the standard formulation of sparse coding (Tibshirani 1996), (Osborne, Presnell, and Turlach 2000) data Y are represented by bases X through the (cid:4) 1 penalized optimization: Here In this formulation there is no positivity constraint on the α (cid”
The Application of Compressed Sensing for Photo-Acoustic Tomography (2009, background): “algorithm [27] presented in Section VII.”
On the non‐negative garrotte estimator (2007, methodology): “It has been demonstrated in Zou and Hastie (2005) that the elastic net often enjoys better prediction performance than both the lasso and ridge regression in simulations.”
Recovering Sparse Signals With a Certain Family of Nonconvex Penalties and DC Programming (2009, neutral): “This success story comes from the fact that the problem can be easily solved either by quadratic programming approach [40], [43], homotopy approaches [34], coordinate wise optimization [22], or gradient projection method [19].”
The solution path of the generalized lasso (2010, background): “The least angle regression (LARS) algorithm, on the other hand, is unique in that it solves (1) for all λ ∈ [0 , ∞ ] [11] (see also the earlier homotopy method of [23], and the even earlier work of [3]). possible This is because the lasso solution is piecewise linear with respect to λ .”
Assumptionless consistency of the Lasso (2013, background): “[25], Knight and Fu [19], Fan and Li [15], Meinshausen and Bühlmann [23], Yuan and Lin [30], Zhao and Yu [33], Zou [34], Greenshtein and Ritov [17], Bunea et.”
Probing the Pareto Frontier for Basis Pursuit Solutions (2008, background): “A number of approaches have been suggested for solving (BP σ ), many of which are based on repeatedly solving (QP λ ) for various values of λ. Notable examples of this approach are Homotopy [40] [41] and Lars [25], which solve (QP λ ) for essentially all values of λ.”
A Modified Principal Component Technique Based on the LASSO (2003, methodology): “Osborne, Presnell, and Turlach (2000) gave an ef cient procedure, based on convex programming and a dual problem, for implementing the LASSO in the regression context.”
Penalized regression, standard errors, and Bayesian lassos (2010, methodology): “For the computation of the lasso, Osborne et al. (2000a) proposed two algorithms.”
A review of unsupervised feature selection methods (2019, methodology): “In this method, the idea is to optimize the Gaussian mixture model via the EM clustering algorithm, where the Maximization-step of this algorithm was reformulated as a l1-constraint LASSO problem (Tibshirani 1996; Osborne et al. 2000).”
The generalized LASSO (2004, methodology): “Right: same situation for Huber's robust loss function. given in [6]: since is a descent direction for the augmented problem, we have On the other hand, feasibility for (31) requires that .”
Rate Minimaxity of the Lasso and Dantzig Selector for the lq Loss in lr Balls (2010, methodology): “The Lasso has the interpretation as boosting(Freund and Schapire, 1996; Friedman, Hastie, and Tibshirani, 2000) and is computationally feasible for high-dimensional data (Osborne, Presnell, and Turlach, 2000a,b; Efron, Hastie, Johnstone, and Tibshirani, 2004).”
Structured Variable Selection with Sparsity-Inducing Norms (2009, background): “he elastic-net penalty (Zou and Hastie, 2005), whose effect is to notably ensure strong convexity. For more sophisticated uniqueness conditions that we have not explored here, we refer the readers to Osborne et al. (2000, Theorem 1, 4 and 5), Rosset et al. (2004, Theorem 5) or Dossal (2007, Theorem ”
SIMULTANEOUS ANALYSIS OF LASSO AND DANTZIG SELECTOR (2008, methodology): “We refer to [9, 18, 19, 22] for detailed discussion of these optimization problems and fast algorithms.”
Approximation accuracy, gradient methods, and error bound for structured convex optimization (2010, background): “Homotopy approaches have been proposed to follow the solution as τ varies between 0 and ∞ [55,66,111,108].”