Open AccessProceedings Article
Polar Operators for Structured Sparse Estimation
Xinhua Zhang,Yaoliang Yu,Dale Schuurmans +2 more
- 05 Dec 2013
- Vol. 26, pp 82-90
TL;DR: A rich class of structured sparse regularizers whose polar operator can be evaluated efficiently is uncovered, and a simple conditional gradient method can be developed that significantly reduces training time vs. the state of the art.
read more
Abstract: Structured sparse estimation has become an important technique in many areas of data analysis. Unfortunately, these estimators normally create computational difficulties that entail sophisticated algorithms. Our first contribution is to uncover a rich class of structured sparse regularizers whose polar operator can be evaluated efficiently. With such an operator, a simple conditional gradient method can then be developed that, when combined with smoothing and local optimization, significantly reduces training time vs. the state of the art. We also demonstrate a new reduction of polar to proximal maps that enables more efficient latent fused lasso.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
•Journal Article
Generalized Conditional Gradient for Sparse Estimation
TL;DR: In this paper, the generalized conditional gradient (GCGGCG) algorithm for solving sparse optimization problems has been investigated and shown to provide a more efficient alternative to current state-of-the-art approaches.
•Posted Content
Generalized Conditional Gradient for Sparse Estimation
TL;DR: In this paper, the generalized conditional gradient (GCGGCG) algorithm was investigated for solving structured sparse optimization problems, and it can provide a more efficient alternative to current state-of-the-art approaches.
48
•Proceedings Article
Parallel and distributed block-coordinate frank-wolfe algorithms
Yu-Xiang Wang,Veeranjaneyulu Sadhanala,Wei Dai,Willie Neiswanger,Suvrit Sra,Eric P. Xing +5 more
- 19 Jun 2016
TL;DR: In this article, the authors study parallel and distributed Frank-Wolfe algorithms on shared memory machines with mini-batching, and the latter in a delayed update framework, and show significant speedups over competing state-of-the-art (and synchronous) methods.
•Proceedings Article
Structured estimation with atomic norms: general bounds and applications
Sheng Chen,Arindam Banerjee +1 more
- 07 Dec 2015
TL;DR: This paper presents general upper bounds for such geometric measures, which only require simple information of the atomic norm under consideration, and establishes tightness of these bounds by providing the corresponding lower bounds.
•Proceedings Article
Structured Matrix Recovery via the Generalized Dantzig Selector
Sheng Chen,Arindam Banerjee +1 more
- 01 Jan 2016
TL;DR: This paper presents non-asymptotic analysis for estimation of generally structured matrices via the generalized Dantzig selector under generic sub-Gaussian measurements and shows that the estimation error can always be succinctly expressed in terms of a few geometric measures of suitable sets which only depend on the structure of the underlying true matrix.
References
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Amir Beck,Marc Teboulle +1 more
TL;DR: A new fast iterative shrinkage-thresholding algorithm (FISTA) which preserves the computational simplicity of ISTA but with a global rate of convergence which is proven to be significantly better, both theoretically and practically.
14.3K
•Book
Theory of Linear and Integer Programming
Alexander Schrijver
- 01 Dec 1986
TL;DR: Introduction and Preliminaries.
A Gene-Expression Signature as a Predictor of Survival in Breast Cancer
Marc J. van de Vijver,Yudong D. He,Laura J. van't Veer,Hongyue Dai,Augustinus A. M. Hart,D.W. Voskuil,George J. Schreiber,Johannes L. Peterse,Christopher J. Roberts,Matthew J. Marton,Mark Parrish,Douwe Atsma,Anke T. Witteveen,Annuska M. Glas,Leonie J. M. J. Delahaye,Tony van de Velde,Harry Bartelink,Sjoerd Rodenhuis,Emiel J. Th. Rutgers,Stephen H. Friend,René Bernards +20 more
TL;DR: The gene-expression profile studied is a more powerful predictor of the outcome of disease in young patients with breast cancer than standard systems based on clinical and histologic criteria.
Smooth minimization of non-smooth functions
TL;DR: A new approach for constructing efficient schemes for non-smooth convex optimization is proposed, based on a special smoothing technique, which can be applied to functions with explicit max-structure, and can be considered as an alternative to black-box minimization.
Sparsity and smoothness via the fused lasso
TL;DR: The fused lasso is proposed, a generalization that is designed for problems with features that can be ordered in some meaningful way, and is especially useful when the number of features p is much greater than N, the sample size.