The incoherence condition in additive models

author: Sara van de Geer, ETH Zurich
published: Dec. 18, 2008,   recorded: December 2008,   views: 573
Categories

Slides

Related Open Educational Resources

Related content

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Lecture popularity: You need to login to cast your vote.
  Bibliography

Description

We extend the idea of regularization using the Lasso, to the case of an additive model with p components, p being larger than the sample size n. Our method has a group Lasso type structure, and penalizes non-smoothness of the components in the additive model. To arrive at a sparsity oracle in- equality, we need an incoherence condition which generalizes the incoherence conditions used for the Lasso. Bickel et al. (2008) impose the “restricted eigenvalue assumption”, which is closely related to the “compatibility con- dition” in van de Geer (2007), which we simply call “Condition C”. We will formulate a version of such a “Condition C” for additive models. To verify it, we discuss the case of random design. We prove new results for weighted empirical processes, which make the transition from random to fixed design possible, and which only requires a population version of “Condition C”. A consequence is that the sparsity oracle property of our procedure holds when the variables are independent,andthatalsovariousdependencystructuresare allowed.

See Also:

Download slides icon Download slides: sip08_geer_ticiam_01.pdf (321.4 KB)


Help icon Streaming Video Help

Link this page

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !

Write your own review or comment:

make sure you have javascript enabled or clear this field: