Browsing by Author "Pilanci, M."

Now showing 1 - 4 of 4

Open Access
Expectation maximization based matching pursuit
(IEEE, 2012) Gurbuz, A.C.; Pilanci, M.; Arıkan, Orhan
A novel expectation maximization based matching pursuit (EMMP) algorithm is presented. The method uses the measurements as the incomplete data and obtain the complete data which corresponds to the sparse solution using an iterative EM based framework. In standard greedy methods such as matching pursuit or orthogonal matching pursuit a selected atom can not be changed during the course of the algorithm even if the signal doesn't have a support on that atom. The proposed EMMP algorithm is also flexible in that sense. The results show that the proposed method has lower reconstruction errors compared to other greedy algorithms using the same conditions. © 2012 IEEE.
Open Access
M-IHS: An accelerated randomized preconditioning method avoiding costly matrix decompositions
(Elsevier Inc., 2023-08-29) Ozaslan, I. K.; Pilanci, M.; Arıkan, Orhan
Momentum Iterative Hessian Sketch ([Formula presented]) techniques, a group of solvers for large scale regularized linear Least Squares (LS) problems, are proposed and analyzed in detail. The proposed [Formula presented] techniques are obtained by incorporating Polyak's heavy ball acceleration into the Iterative Hessian Sketch algorithm and they provide significant improvements over the randomized preconditioning techniques. By solving the linear systems arising in the sub-problems during the iterations approximately, the proposed techniques are capable of avoiding all matrix decompositions and inversions, which is one of the main advantages over the alternative solvers such as the Blendenpik and the LSRN. Similar to the Chebyshev semi-iterations, the [Formula presented] variants do not use any inner products and eliminate the corresponding synchronization steps in hierarchical or distributed memory systems, yet the [Formula presented] converges faster than the Chebyshev semi-iteration based solvers. Lower bounds on the required sketch size for various randomized distributions are established through the error analyses. Unlike the previously proposed approaches to produce a solution approximation, the proposed [Formula presented] techniques can use sketch sizes that are proportional to the statistical dimension which is always smaller than the rank of the coefficient matrix. © 2023 Elsevier Inc.
Open Access
Recovery of sparse perturbations in Least Squares problems
(IEEE, 2011) Pilanci, M.; Arıkan, Orhan
We show that the exact recovery of sparse perturbations on the coefficient matrix in overdetermined Least Squares problems is possible for a large class of perturbation structures. The well established theory of Compressed Sensing enables us to prove that if the perturbation structure is sufficiently incoherent, then exact or stable recovery can be achieved using linear programming. We derive sufficiency conditions for both exact and stable recovery using known results of ℓ 0/ℓ 1 equivalence. However the problem turns out to be more complicated than the usual setting used in various sparse reconstruction problems. We propose and solve an optimization criterion and its convex relaxation to recover the perturbation and the solution to the Least Squares problem simultaneously. Then we demonstrate with numerical examples that the proposed method is able to recover the perturbation and the unknown exactly with high probability. The performance of the proposed technique is compared in blind identification of sparse multipath channels. © 2011 IEEE.
Open Access
Structured least squares problems and robust estimators
(IEEE, 2010-10-22) Pilanci, M.; Arıkan, Orhan; Pinar, M. C.
A novel approach is proposed to provide robust and accurate estimates for linear regression problems when both the measurement vector and the coefficient matrix are structured and subject to errors or uncertainty. A new analytic formulation is developed in terms of the gradient flow of the residual norm to analyze and provide estimates to the regression. The presented analysis enables us to establish theoretical performance guarantees to compare with existing methods and also offers a criterion to choose the regularization parameter autonomously. Theoretical results and simulations in applications such as blind identification, multiple frequency estimation and deconvolution show that the proposed technique outperforms alternative methods in mean-squared error for a significant range of signal-to-noise ratio values.