Download Algorithms for Sparsity-Constrained Optimization by Sohail Bahmani PDF

By Sohail Bahmani

This thesis demonstrates strategies that supply swifter and extra actual options to various difficulties in computer studying and sign processing. the writer proposes a "greedy" set of rules, deriving sparse recommendations with promises of optimality. using this set of rules gets rid of some of the inaccuracies that happened with using prior models.

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2. Note that the functions that satisfy the SRH are convex over canonical sparse subspaces, but they are not necessarily convex everywhere. The following two examples describe some non-convex functions that have SRH. 1. x/ D 12 xT Qx, where Q D 2 11T I. x/ D Q. 3) determine the extreme eigenvalues across all of the k k symmetric submatrices of Q. Note that the diagonal entries of Q are all equal to one, while its off-diagonal entries are all equal to two. Therefore, for any 1-sparse signal u we have uT Qu D kuk22 , meaning that f has 1 -SRH with T T 1 D 1.

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Princeton University Press, Princeton, NJ, 1994. T. Hastie, R. Tibshirani, and J. H. Friedman. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Verlag, 2009. A. Jalali, C. C. Johnson, and P. K. Ravikumar. On learning discrete graphical models using greedy methods. In J. Shawe-Taylor, R. S. Zemel, P. Bartlett, F. C. N. Pereira, and K. Q. Weinberger, editors, Advances in Neural Information Processing Systems, volume 24, pages 1935–1943. 2011. S. M. Kakade, O.

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