Abstract
In This Paper, the Effect of Dimensionality on the Supervised Learning of Infinitely Differentiable Regression Functions is Analyzed. by Invoking the Van Trees Lower Bound, We Prove Lower Bounds on the Generalization Error with Respect to the Number of Samples and the Dimensionality of the Input Space Both in a Linear and Non-Linear Context. It is Shown that in Non-Linear Problems Without Prior Knowledge, the Curse of Dimensionality is a Serious Problem. at the Same Time, We Speculate Counter-Intuitively that Sometimes Supervised Learning Becomes Plausible in the Asymptotic Limit of Infinite Dimensionality. © 2011 Springer Science business Media, LLC.
Recommended Citation
E. Liitiäinen et al., "On the Curse of Dimensionality in Supervised Learning of Smooth Regression Functions," Neural Processing Letters, vol. 34, no. 2, pp. 133 - 154, Springer, Oct 2011.
The definitive version is available at https://doi.org/10.1007/s11063-011-9188-7
Department(s)
Engineering Management and Systems Engineering
Keywords and Phrases
Analytic function; High dimensional; Minimax; Nonparametric regression; Supervised learning; Van Trees
International Standard Serial Number (ISSN)
1573-773X; 1370-4621
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2024 The Authors, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
01 Oct 2011
