
doi: 10.3934/mine.2022053
<abstract><p>Despite recent advances in regularization theory, the issue of parameter selection still remains a challenge for most applications. In a recent work the framework of statistical learning was used to approximate the optimal Tikhonov regularization parameter from noisy data. In this work, we improve their results and extend the analysis to the elastic net regularization. Furthermore, we design a data-driven, automated algorithm for the computation of an approximate regularization parameter. Our analysis combines statistical learning theory with insights from regularization theory. We compare our approach with state-of-the-art parameter selection criteria and show that it has superior accuracy.</p></abstract>
T57-57.97, Applied mathematics. Quantitative methods, Learning and adaptive systems in artificial intelligence, sub-gaussian vectors, elastic net data-driven regularization, noisy data, matrix concentration inequality, optimal Tikhonov regularization parameter, sub-Gaussian vector, iterative thresholding, parameter selection, Stochastic and other probabilistic methods applied to problems in solid mechanics, data-driven regularization, matrix concentration inequalities, Thin bodies, structures, statistical learnin, elastic net regularization
T57-57.97, Applied mathematics. Quantitative methods, Learning and adaptive systems in artificial intelligence, sub-gaussian vectors, elastic net data-driven regularization, noisy data, matrix concentration inequality, optimal Tikhonov regularization parameter, sub-Gaussian vector, iterative thresholding, parameter selection, Stochastic and other probabilistic methods applied to problems in solid mechanics, data-driven regularization, matrix concentration inequalities, Thin bodies, structures, statistical learnin, elastic net regularization
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