Sara van de Geer - Compatibility and the Lasso
From Katie Gentilello September 10th, 2018
Related Media
We will see in the first lecture that one needs conditions which relate the penalty to the risk function. They have in a certain sense to be “compatible”. We discuss these compatibility conditions in the second lecture in the context of the Lasso, where the L1-penalty needs to be compatible with the least squares risk, i.e. with the L2-norm. We give as example the total variation penalty. For D := {x1,…,xn} ⊂ R an increasing sequence, the total variation of a function f : D -> R is the sum of the absolute values of its jump sizes. We derive compatibility and as a consequence a sparsity oracle inequality which shows adaptation to the number of jumps.
- Tags
- name
- Sara van de Geer
- biography
- Sara van de Geer has been Full Professor at the Seminar for Statistics at ETH Zurich since September 2005. Her main field of research is mathematical statistics, with special interest in high-dimensional problems.
- Date
- September 4th, 2018
- Appears In