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Download Algorithms for Sparsity-Constrained Optimization by Sohail Bahmani PDF

By Sohail Bahmani

This thesis demonstrates innovations that offer swifter and extra exact ideas to numerous difficulties in laptop studying and sign processing. the writer proposes a "greedy" set of rules, deriving sparse strategies with promises of optimality. using this set of rules eliminates a few of the inaccuracies that happened with using prior models.

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Schuurmans, J. Lafferty, C. K. I. Williams, and A. Culotta, editors, Advances in Neural Information Processing Systems, volume 22, pages 1348–1356. 2009. ST]. Y. Nesterov. Efficiency of coordinate descent methods on huge-scale optimization problems. SIAM Journal on Optimization, 22(2):341–362, Jan. 2012. S. Shalev-Shwartz, N. Srebro, and T. Zhang. Trading accuracy for sparsity in optimization problems with sparsity constraints. SIAM Journal on Optimization, 20(6):2807–2832, 2010. A. Tewari, P. K.

In contrast, the multiplier in our results is fixed at 4, independent of the objective function itself, and we make no assumptions about the magnitudes of the non-zero entries. In this chapter we propose a non-convex greedy algorithm, the Gradient Support Pursuit (GraSP), for sparse estimation problems that arise in applications with general nonlinear models. We prove the accuracy of GraSP for a class of cost functions that have a Stable Restricted Hessian (SRH). The SRH characterizes the functions whose restriction to sparse canonical subspaces have well-conditioned Hessian matrices.

Sparse approximate solutions to linear systems. SIAM Journal on Computing, 24(2):227–234, 1995. D. Needell and J. A. Tropp. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Applied and Computational Harmonic Analysis, 26(3):301–321, 2009. Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad. Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition. In Conference Record of the 27th Asilomar Conference on Signals, Systems and Computers, volume 1, pages 40–44, Pacific Grove, CA, Nov.

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