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Cited by 196

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

Huan Xu, Caramanis, C., Mannor, S.·2012·IEEE Transactions on Pattern Analysis and Machine Intelligence
DOI 10.1109/tpami.2011.177
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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 ℓ(1)-regularized regression (Lasso) cannot be stable, while ℓ(2)-regularized regression is known to have strong stability properties and is therefore not sparse.

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Metadata

Authors
Xu, H., Caramanis, C., & Mannor, S.
Venue
IEEE Transactions on Pattern Analysis and Machine Intelligence
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Published
2012-01
Volume
34
Issue
1
Pages
187-193
ISSN
  • 0162-8828 (ISSN-L)
  • 2160-9292
DOI
10.1109/tpami.2011.177
OpenAlex
W2035820295
Cited by
196
References
0
FWCI
10.02
Type
journal article
Language
en
Open access
closed

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CoChat. (2026). Citation check: Sparse Algorithms Are Not Stable: A No-Free-Lunch Theorem. https://app.cochat.ai/papers/10.1109/tpami.2011.177
The paper
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. https://doi.org/10.1109/tpami.2011.177

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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.