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.