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A Unified Framework for Sparse Relaxed Regularized Regression: SR3 | IEEE Journals & Magazine | IEEE Xplore

A Unified Framework for Sparse Relaxed Regularized Regression: SR3


Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. We propose a unified framework for sparse relaxed regular...

Abstract:

Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression, in particular, has been instrumental i...Show More

Abstract:

Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression, in particular, has been instrumental in scientific model discovery, including compressed sensing applications, variable selection, and high-dimensional analysis. We propose a broad framework for sparse relaxed regularized regression, called SR3. The key idea is to solve a relaxation of the regularized problem, which has three advantages over the state-of-the-art: 1) solutions of the relaxed problem are superior with respect to errors, false positives, and conditioning; 2) relaxation allows extremely fast algorithms for both convex and nonconvex formulations; and 3) the methods apply to composite regularizers, essential for total variation (TV) as well as sparsity-promoting formulations using tight frames. We demonstrate the advantages of SR3 (computational efficiency, higher accuracy, faster convergence rates, and greater flexibility) across a range of regularized regression problems with synthetic and real data, including applications in compressed sensing, LASSO, matrix completion, TV regularization, and group sparsity. Following standards of reproducible research, we also provide a companion MATLAB package that implements these examples.
Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. We propose a unified framework for sparse relaxed regular...
Published in: IEEE Access ( Volume: 7)
Page(s): 1404 - 1423
Date of Publication: 12 December 2018
Electronic ISSN: 2169-3536

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