By Sohail Bahmani
This thesis demonstrates recommendations that supply swifter and extra exact strategies to quite a few difficulties in desktop studying and sign processing. the writer proposes a "greedy" set of rules, deriving sparse options with promises of optimality. using this set of rules gets rid of a number of the inaccuracies that happened with using past models.
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Additional info for Algorithms for Sparsity-Constrained Optimization
Shechtman, Y. C. Eldar, A. Szameit, and M. Segev. Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing. Optics Express, 19(16):14807–14822, July 2011a. Y. Shechtman, A. Szameit, E. Osherovic, E. Bullkich, H. Dana, S. Gazit, S. Shoham, M. Zibulevsky, I. Yavneh, E. B. Kley, Y. C. Eldar, O. Cohen, and M. Segev. Sparsity-based single-shot sub-wavelength coherent diffractive imaging. In Frontiers in Optics, OSA Technical Digest, page PDPA3. Optical Society of America, Oct.
References A. Agarwal, S. Negahban, and M. Wainwright. Fast global convergence rates of gradient methods for high-dimensional statistical recovery. In J. Lafferty, C. K. I. Williams, J. ShaweTaylor, R. Zemel, and A. Culotta, editors, Advances in Neural Information Processing Systems, volume 23, pages 37–45. 2010. ML]. A. Beck and Y. C. Eldar. Sparsity constrained nonlinear optimization: Optimality conditions and algorithms. IT], Mar. 2012. P. Bickel, Y. Ritov, and A. Tsybakov. Simultaneous analysis of Lasso and Dantzig selector.
The results of both GraSP methods with “debiasing” are also included. The average loss at the true parameter and one standard p deviation interval around it are plotted as well. 5 Simulations 29 c ρ = 1/2 d ρ= √ 2/2 Fig. 1 (continued) on the plots. Furthermore, we evaluated performance of GraSP with the debiasing procedure described in Sect. 1. As can be seen from the figure at lower values of the sampling ratio GraSP is not accurate and does not seem to be converging. This behavior can be explained by the fact that without regularization at low sampling ratios the training data is 30 3 Sparsity-Constrained Optimization linearly separable or has very few mislabelled samples.