A Second-Order Perceptron Algorithm

Abstract

We introduce a variant of the Perceptron algorithm called second-order Perceptron algorithm, which is able to exploit certain spectral properties of the data. We analyze the second-order Perceptron algorithm in the mistake bound model of on-line learning and prove bounds in terms of the eigenvalues of the Gram matrix created from the data. The performance of the second-order Perceptron algorithm is affected by the setting of a parameter controlling the sensitivity to the distribution of the eigenvalues of the Gram matrix. Since this information is not preliminarly available to on-line algorithms, we also design a refined version of the second-order Perceptron algorithm which adaptively sets the value of this parameter. For this second algorithm we are able to prove mistake bounds corresponding to a nearly optimal constant setting of the parameter.

Cite

Text

Cesa-Bianchi et al. "A Second-Order Perceptron Algorithm." Annual Conference on Computational Learning Theory, 2002. doi:10.1007/3-540-45435-7_9

Markdown

[Cesa-Bianchi et al. "A Second-Order Perceptron Algorithm." Annual Conference on Computational Learning Theory, 2002.](https://mlanthology.org/colt/2002/cesabianchi2002colt-second/) doi:10.1007/3-540-45435-7_9

BibTeX

@inproceedings{cesabianchi2002colt-second,
  title     = {{A Second-Order Perceptron Algorithm}},
  author    = {Cesa-Bianchi, Nicolò and Conconi, Alex and Gentile, Claudio},
  booktitle = {Annual Conference on Computational Learning Theory},
  year      = {2002},
  pages     = {121-137},
  doi       = {10.1007/3-540-45435-7_9},
  url       = {https://mlanthology.org/colt/2002/cesabianchi2002colt-second/}
}