Download PDF by Sohail Bahmani: Algorithms for Sparsity-Constrained Optimization

By Sohail Bahmani

ISBN-10: 3319018809

ISBN-13: 9783319018805

ISBN-10: 3319018817

ISBN-13: 9783319018812

This thesis demonstrates recommendations that offer quicker and extra actual options to numerous difficulties in desktop studying and sign processing. the writer proposes a "greedy" set of rules, deriving sparse ideas 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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Extra resources for Algorithms for Sparsity-Constrained Optimization

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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. Ravikumar, and I. S. Dhillon. Greedy algorithms for structurally constrained high dimensional problems. In J. Shawe-Taylor, R. Zemel, P. Bartlett, F. Pereira, and K. Weinberger, editors, Advances in Neural Information Processing Systems, volume 24, pages 882–890. 2011. J. A. Tropp. User-friendly tail bounds for sums of random matrices.

2009) where regularization with “decomposable” norms is considered in M-estimation problems. To provide the accuracy guarantees, these works generalize the Restricted Eigenvalue condition Bickel et al. (2009) to ensure that the loss function is strongly convex over a restriction of its domain. We would like to emphasize that these sufficient conditions generally hold with proper constants and with high probability only if one assumes that the true parameter is bounded. , Bunea 2008; Kakade et al.

Dahmen, and R. DeVore. Compressed sensing and best k-term approximation. Journal of American Mathematical Society, 22(1):211–231, Jan. 2009. 10 2 Preliminaries W. Dai and O. Milenkovic. Subspace pursuit for compressive sensing signal reconstruction. IEEE Transactions on Information Theory, 55(5):2230–2249, 2009. A. J. Dobson and A. Barnett. An Introduction to Generalized Linear Models. Chapman and Hall/CRC, Boca Raton, FL, 3rd edition, May 2008. ISBN 9781584889502. D. L. Donoho. Compressed sensing.

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Algorithms for Sparsity-Constrained Optimization by Sohail Bahmani


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