Abstract
Boosting converts weak hypotheses with a small edge over random guessing into highly accurate predictors, but the expressive power of the resulting classifier can depend strongly on the structure of the base class. We study this phenomenon through the $γ$-VC dimension introduced by Alon et al. (STOC 2021). Our first result shows that this parameter characterizes the sample complexity for weak-to-strong learning up to a constant factor scaling in $γ$. We then sharpen the general relationship between the classic VC dimension and the $γ$-VC dimension. Finally, we also give improved upper and lower bounds on the $γ$-VC dimension for the fundamental concept classes of decision stumps and axis-parallel rectangles in $\mathbb{R}^d$.
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Publication details
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- Green open access
Cite this article
APA 7
Cunha, A. D., Larsen, K. G., & Zou, L. Y. (2026). Boosting and the Expressive Power of Simple Weak Learners via the $γ$-VC Dimension. https://omanscience.com/en/articles/boosting-and-the-expressive-power-of-simple-weak-learners-via-the-vc-dimension
MLA 9
Cunha, Arthur da, et al. "Boosting and the Expressive Power of Simple Weak Learners via the $γ$-VC Dimension." https://omanscience.com/en/articles/boosting-and-the-expressive-power-of-simple-weak-learners-via-the-vc-dimension.
Chicago (author–date)
Cunha, Arthur da, Kasper Green Larsen, and Liang-Yu Zou. 2026. "Boosting and the Expressive Power of Simple Weak Learners via the $γ$-VC Dimension." https://omanscience.com/en/articles/boosting-and-the-expressive-power-of-simple-weak-learners-via-the-vc-dimension.
Harvard
Cunha, A. D., Larsen, K. G. and Zou, L. Y. (2026) 'Boosting and the Expressive Power of Simple Weak Learners via the $γ$-VC Dimension', Available at: https://omanscience.com/en/articles/boosting-and-the-expressive-power-of-simple-weak-learners-via-the-vc-dimension.
Vancouver
Cunha AD, Larsen KG, Zou LY. Boosting and the Expressive Power of Simple Weak Learners via the $γ$-VC Dimension. https://omanscience.com/en/articles/boosting-and-the-expressive-power-of-simple-weak-learners-via-the-vc-dimension
IEEE
A. D. Cunha, K. G. Larsen, and L. Y. Zou, "Boosting and the Expressive Power of Simple Weak Learners via the $γ$-VC Dimension," https://omanscience.com/en/articles/boosting-and-the-expressive-power-of-simple-weak-learners-via-the-vc-dimension.