Greedy Algorithms for Structurally Constrained High Dimensional Problems

By Ambuj Tewari, Pradeep Ravikumar, Inderjit S. Dhillon. 2011

115 citations recorded by the source corpus.

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Citations in the corpus

Introduction to Online Convex Optimization (2016, methodology): “Due to the applicability of the FW algorithm to large-scale constrained problems, it has been a method of choice in recent machine learning applications, to name a few: (61; 69; 60; 39; 50; 58; 98; 16; 104; 46; 47; 18).”
A Convex Atomic-Norm Approach to Multiple Sequence Alignment and Motif Discovery (2016, background): “The problem of minimizing convex, smooth function subject to a feasible domain being convex hull of atomic set has been widely studied in the recent years (Jaggi, 2013; Tewari et al., 2011), where one can exploit the specific structure of atomic set S to find search direction efficiently (Jaggi, 201”
On Solutions of Sparsity Constrained Optimization (2015, methodology): “Later, various variants of RSC and RSS were developed and used in [4–7] to guarantee the existence of unique solution and corresponding error bound holding for SCO.”
Differentially Private Matrix Completion, Revisited (2017, methodology): “Frank-Wolfe based method: We use the standard nuclear norm formulation (Recht, 2011; Shalev-shwartz et al., 2011; Tewari et al., 2011; Candes & Recht, 2012) for the matrix completion problem:”
Collaborative Filtering with Graph Information: Consistency and Scalable Methods (2015, methodology): “A quick note on solving (15): since k · kA is a weighted nuclear norm, one can resort to proximal point methods [6], or greedy methods developed specifically for atomic norm constrained minimization [18, 22].”
Restricted Strong Convexity Implies Weak Submodularity (2016, methodology): “Greedy methods for sparsity constrained regression were analyzed in [14, 15, 18, 21, 22, 23] under assumptions similar to ours but without connections to submodularity.”
Non-convex Optimization for Machine Learning (2017, unknown): “There exist works [Tewari et al., 2011] that give generic methods to perform sparse recovery in such structurally constrained settings.”
Revisiting Frank-Wolfe: Projection-Free Sparse Convex Optimization (2013, methodology): “(Tewari et al., 2011) and (Dudik et al., 2012, Appendix D) have recently studied Frank- Wolfe methods for atomic domains using similar ideas as in (Jaggi, 2011), but obtaining weaker convergence results.”