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|Title:||Sparse algorithms are not stable: A no-free-lunch theorem|
|Authors:||Xu, H. |
|Citation:||Xu, H., Caramanis, C., Mannor, S. (2012). Sparse algorithms are not stable: A no-free-lunch theorem. IEEE Transactions on Pattern Analysis and Machine Intelligence 34 (1) : 187-193. ScholarBank@NUS Repository. https://doi.org/10.1109/TPAMI.2011.177|
|Abstract:||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. © 2012 IEEE.|
|Source Title:||IEEE Transactions on Pattern Analysis and Machine Intelligence|
|Appears in Collections:||Staff Publications|
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