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This paper introduces the "effective dimension," a novel metric designed to empirically estimate learning performance by linking problem properties to average-case outcomes, offering a practical alternative to the theoretical VC dimension. The research quantifies how specific techniques like constructive induction and noise filtering impact learning systems, demonstrating their diminishing returns as target concept complexity increases.
Quantifying the Value of Constructive Induction, Knowledge, and Noise Filtering on Inductive Learning
arXiv:2610.02615v1 Announce Type: new Abstract: Learning research, as one of its central goals, tries to measure, model, and understand how learning-problem properties affect average-case learning performance. For example, we would like to quantify the value of constructive induction, noise filtering, and background knowledge. This paper describes the effective dimension, a new learning measure that helps link problem properties to learning performance. Like the Vapnik-Chervonenkis (VC) dimension, the effective dimension is often in a simple linear relation with problem properties. Unlike the VC dimension, the effective dimension can be estimated empirically and makes average-case predictions. It is therefore more widely applicable to machine and human learning research. The measure is demonstrated on several learning systems including Backpropagation. Finally, the measure is used to precisely predict the benefit of using FRINGE, a feature construction system. The benefit is found to decrease as the complexity of the target concept increases.
Abstract:Learning research, as one of its central goals, tries to measure, model, and understand how learning-problem properties affect average-case learning performance. For example, we would like to quantify the value of constructive induction, noise filtering, and background knowledge. This paper describes the effective dimension, a new learning measure that helps link problem properties to learning performance. Like the Vapnik-Chervonenkis (VC) dimension, the effective dimension is often in a simple linear relation with problem properties. Unlike the VC dimension, the effective dimension can be estimated empirically and makes average-case predictions. It is therefore more widely applicable to machine and human learning research. The measure is demonstrated on several learning systems including Backpropagation. Finally, the measure is used to precisely predict the benefit of using FRINGE, a feature construction system. The benefit is found to decrease as the complexity of the target concept increases.
12 pages, including a modern cover note and the unchanged 11-page author manuscript from 1991. Extended author version of a paper published in Machine Learning Proceedings 1991 (ICML 1991), pp. 153-157. Deposited in arXiv in 2026
Machine Learning (cs.LG)
arXiv:2610.02615 [cs.LG]
(or arXiv:2610.02615v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.02615 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
Machine Learning Proceedings 1991, Morgan Kaufmann, pp. 153-157 (1991)
https://doi.org/10.1016/B978-1-55860-200-7.50034-9 Focus to learn more DOI(s) linking to related resources
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