By Topic

Sparse Algorithms Are Not Stable: A No-Free-Lunch Theorem

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Huan Xu ; National University of Singapore, Singapore ; Constantine Caramanis ; Shie Mannor

We consider two desired properties of learning algorithms: sparsity and algorithmic stability. Both properties are believed to lead to good generalization ability. We show that these two properties are fundamentally at odds with each other: A sparse algorithm cannot be stable and vice versa. Thus, one has to trade off sparsity and stability in designing a learning algorithm. In particular, our general result implies that ℓ1-regularized regression (Lasso) cannot be stable, while ℓ2-regularized regression is known to have strong stability properties and is therefore not sparse.

Published in:

IEEE Transactions on Pattern Analysis and Machine Intelligence  (Volume:34 ,  Issue: 1 )