Linear regression when not only Y is perturbed by noise, but also the very model is assumed to have noise

Sophie M. Fosson, Vito Cerone, Diego Regruto, Sparse linear regression from perturbed data, . Automatica, Volume 122, 2020, DOI: 10.1016/j.automatica.2020.109284.

The problem of sparse linear regression is relevant in the context of linear system identification from large datasets. When data are collected from real-world experiments, measurements are always affected by perturbations or low-precision representations. However, the problem of sparse linear regression from fully-perturbed data is scarcely studied in the literature, due to its mathematical complexity. In this paper, we show that, by assuming bounded perturbations, this problem can be tackled by solving low-complex ℓ2 and ℓ1 minimization problems. Both theoretical guarantees and numerical results are illustrated.

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