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General performance metrics for the LASSO

Abbasi, Ehsan and Thrampoulidis, Christos and Hassibi, Babak (2016) General performance metrics for the LASSO. In: 2016 IEEE Information Theory Workshop (ITW). IEEE , Piscataway, NJ, pp. 181-185. ISBN 978-1-5090-1091-2.

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A recent line of work has established accurate predictions of the mean squared-error (MSE) performance of non-smooth convex optimization methods when used to recover structured signals (e.g. sparse, low-rank) from noisy linear (and possibly compressed) observations. Specifically, in a recent paper [15] we precisely characterized the MSE performance of a general class of regularized M-estimators using a framework that is based on Gaussian process methods. Here, we extend the framework to the analysis of a general class of Lipschitz performance metrics, which in addition to the standard MSE, includes the ℓ1-reconstruction error, the probability of successfully identifying whether an element belongs to the support of a sparse signal, the empirical distribution of the error, etc. For concreteness, we primarily focus on the problem of sparse recovery under ℓ1-regularized least-squares (aka LASSO). We illustrate the validity of the theoretical predictions through numerical simulations and discuss the importance of their precise nature in optimally tuning the involved parameters of the reconstruction method.

Item Type:Book Section
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Thrampoulidis, Christos0000-0001-9053-9365
Additional Information:© 2016 IEEE.
Record Number:CaltechAUTHORS:20161102-074552760
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Official Citation:E. Abbasi, C. Thrampoulidis and B. Hassibi, "General performance metrics for the LASSO," 2016 IEEE Information Theory Workshop (ITW), Cambridge, United Kingdom, 2016, pp. 181-185. doi: 10.1109/ITW.2016.7606820
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71674
Deposited By: Ruth Sustaita
Deposited On:02 Nov 2016 15:53
Last Modified:11 Nov 2021 04:49

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