no code implementations • 18 Dec 2023 • Alexander Bastounis, Felipe Cucker, Anders C. Hansen
However, we define a LASSO condition number and design an efficient algorithm for computing these support sets provided the input data is well-posed (has finite condition number) in time polynomial in the dimensions and logarithm of the condition number.
no code implementations • 13 Sep 2023 • Alexander Bastounis, Alexander N. Gorban, Anders C. Hansen, Desmond J. Higham, Danil Prokhorov, Oliver Sutton, Ivan Y. Tyukin, Qinghua Zhou
We consider classical distribution-agnostic framework and algorithms minimising empirical risks and potentially subjected to some weights regularisation.
1 code implementation • 13 Jul 2023 • Johan S. Wind, Vegard Antun, Anders C. Hansen
In this work we provide sharp results for the implicit regularization imposed by the gradient flow of Diagonal Linear Networks (DLNs) in the over-parameterized regression setting and, potentially surprisingly, link this to the phenomenon of phase transitions in generalized hardness of approximation (GHA).
1 code implementation • 20 Jan 2021 • Matthew J. Colbrook, Vegard Antun, Anders C. Hansen
We address this paradox by demonstrating basic well-conditioned problems in scientific computing where one can prove the existence of NNs with great approximation qualities, however, there does not exist any algorithm, even randomised, that can train (or compute) such a NN.
1 code implementation • 5 Jan 2020 • Nina M. Gottschling, Vegard Antun, Anders C. Hansen, Ben Adcock
In inverse problems in imaging, the focus of this paper, there is increasing empirical evidence that methods may suffer from hallucinations, i. e., false, but realistic-looking artifacts; instability, i. e., sensitivity to perturbations in the data; and unpredictable generalization, i. e., excellent performance on some images, but significant deterioration on others.
1 code implementation • 4 Jun 2019 • Laura Thesing, Vegard Antun, Anders C. Hansen
We provide the foundations for such a program establishing the existence of the false structures in practice.
1 code implementation • 14 Feb 2019 • Vegard Antun, Francesco Renna, Clarice Poon, Ben Adcock, Anders C. Hansen
Deep learning, due to its unprecedented success in tasks such as image classification, has emerged as a new tool in image reconstruction with potential to change the field.