Asymptotic Theory for Regularization: One-Dimensional Linear Case

Abstract

The generalization ability of a neural network can sometimes be improved dramatically by regularization. To analyze the improve(cid:173) ment one needs more refined results than the asymptotic distri(cid:173) bution of the weight vector. Here we study the simple case of one-dimensional linear regression under quadratic regularization, i.e., ridge regression. We study the random design, misspecified case, where we derive expansions for the optimal regularization pa(cid:173) rameter and the ensuing improvement. It is possible to construct examples where it is best to use no regularization.

Cite

Text

Koistinen. "Asymptotic Theory for Regularization: One-Dimensional Linear Case." Neural Information Processing Systems, 1997.

Markdown

[Koistinen. "Asymptotic Theory for Regularization: One-Dimensional Linear Case." Neural Information Processing Systems, 1997.](https://mlanthology.org/neurips/1997/koistinen1997neurips-asymptotic/)

BibTeX

@inproceedings{koistinen1997neurips-asymptotic,
  title     = {{Asymptotic Theory for Regularization: One-Dimensional Linear Case}},
  author    = {Koistinen, Petri},
  booktitle = {Neural Information Processing Systems},
  year      = {1997},
  pages     = {294-300},
  url       = {https://mlanthology.org/neurips/1997/koistinen1997neurips-asymptotic/}
}