Regularization Methods for High-Dimensional Data

• Applicant: Professorin Dr. Sara A. van de Geer
• Subject Area: Mathematics
• Term: from 2008 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 40095828

Estimation with ℓ1-penalty, also known as the Lasso, has become extremely popular, as the method is tailored for high-dimensional data, and is computationally very attractive. The theoretical properties of the standard Lasso are by now quite well understood. We will develop new theory for nonlinear models, such as in generalized-linear and semi-parametetric models. One of the goals will be to gain more insight into the variable selection properties of the Lasso and its modifications, such as the group Lasso and the adaptive Lasso. We moreover will further develop the restricted eigenvalue conditions used to prove oracle results, and to refine the arguments for the case of highly correlated design.

• DFG Programme: Research Units
• Subproject of: FOR 916: Statistical Regularisation and Qualitative Constraints - Inference, Algorithms, Asymptotics and Applications
• International Connection: Switzerland