By Sohail Bahmani
This thesis demonstrates ideas that supply quicker and extra actual strategies to quite a few 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 gets rid of a few of the inaccuracies that happened with using past models.
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Extra resources for Algorithms for Sparsity-Constrained Optimization
By analyzing necessary optimality conditions for the sparse minimizer, a few iterative algorithms are proposed in Beck and Eldar (2012) that converge to the sparse minimizer, should the objective satisfy some regularity conditions. Furthermore, Jalali et al. (2011) studied a forward-backward algorithm using a variant of the sufficient conditions introduced in Negahban et al. (2009). Similar to our work, the main result in Jalali et al. (2011) imposes conditions on the function as restricted to sparse inputs whose non-zeros are fewer than a multiple of the target sparsity level.
2009, and references therein). Thus, it is desirable to develop theory and algorithms that apply to a broader class of optimization problems with sparsity constraints. , Bunea 2008; van de Geer 2008; Kakade et al. 2010; Negahban et al. 2009). As a special case, logistic regression with `1 and elastic net regularization are studied by Bunea (2008). Furthermore, Kakade et al. (2010) have studied the accuracy of sparse estimation through `1 -regularization for the exponential family distributions.
I. Williams, J. Shawe-Taylor, R. Zemel, and A. Culotta, editors, Advances in Neural Information Processing Systems, volume 23, pages 37–45. 2010. ML]. A. Beck and M. Teboulle. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1):183–202, 2009. T. Blumensath and M. E. Davies. Iterative hard thresholding for compressed sensing. Applied and Computational Harmonic Analysis, 27(3):265–274, Nov. 2009. P. Boufounos and R. Baraniuk. 1-bit compressive sensing.
Algorithms for Sparsity-Constrained Optimization by Sohail Bahmani