B1920
Title: An overparametrized point of view on nonnegative regression
Authors: Claudio Mayrink Verdun - Technical University of Munich (Germany) [presenting]
Johannes Maly - Ludwig Maximilian University of Munich (Germany)
Heudson Mirandola - Federal University of Rio de Janeiro (Brazil)
Hung-Hsu Chou - Technical University of Munich (Germany)
Abstract: In many applications, solutions of regression problems are required to be non-negative. For example, when one seeks to retrieve pixel intensity values or the chemical concentration of a substance. In this context, nonnegative least squares are a ubiquitous tool. Despite vast efforts, since the seminal work of Lawson and Hanson in the '70s, the nonnegativity assumption is still an obstacle to the scalability of many off-the-shelf solvers. Recently, in a different context, numerous developments have been seen in deep neural networks, where the training of over-parametrized models via gradient descent leads to surprising generalization properties and to the retrieval of regularized solutions such as low-rank matrices. The problem of non-negative least squares is connected with recent progress in the field of implicit bias of gradient descent.
