Skaalattu harva lineaarinen regressio elastisella verkolla
Elias Raninen · Aaltodoc (Aalto University) · 2017
Scaled linear regression is a form of penalized linear regression in which the penalty level is automatically scaled in proportion to the estimated noise level in the data. This makes the penalty parameter independent of the noise scale enabling an analytical approach for choosing an optimal penalty level for a given problem. In this thesis, we first review conventional penalized regression methods, such as ridge regression, lasso, and the elastic net. Then, we review some scaled sparse linear regression methods, the most relevant of which is the scaled lasso, also known as square-root lasso. As an original contribution, we propose two elastic net formulations, which extend the scaled lasso to the elastic net framework. We demonstrate by numerical examples that the proposed estimators improve upon the scaled lasso in the presence of high correlations in the feature space. As a real-world application example, we apply the proposed estimators in a simulated single snapshot direction-of-arrival (DOA) estimation problem, where we show that the proposed estimators perform better, especially when the angles of incidence of the DOAs are oblique with respect to the uniform linear array (ULA) axis.