Hilbertian Metrics and Positive Definite Kernels on Probability Measures
Abstract
We investigate the problem of defining Hilbertian metrics resp.\npositive definite kernels on probability measures, continuing previous work. This type of kernels has shown very good\nresults in text classification and has a wide range of possible\napplications. In this paper we extend the two-parameter family of\nHilbertian metrics of Topsoe such that it now includes all\ncommonly used Hilbertian metrics on probability measures. This\nallows us to do model selection among these metrics in an elegant\nand unified way. Second we investigate further our approach to\nincorporate similarity information of the probability space into\nthe kernel. The analysis provides a better understanding of these\nkernels and gives in some cases a more efficient way to compute\nthem. Finally we compare all proposed kernels in two text and two\nimage classification problems.
Cite
Text
Hein and Bousquet. "Hilbertian Metrics and Positive Definite Kernels on Probability Measures." Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics, 2005.Markdown
[Hein and Bousquet. "Hilbertian Metrics and Positive Definite Kernels on Probability Measures." Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics, 2005.](https://mlanthology.org/aistats/2005/hein2005aistats-hilbertian/)BibTeX
@inproceedings{hein2005aistats-hilbertian,
title = {{Hilbertian Metrics and Positive Definite Kernels on Probability Measures}},
author = {Hein, Matthias and Bousquet, Olivier},
booktitle = {Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics},
year = {2005},
pages = {136-143},
volume = {R5},
url = {https://mlanthology.org/aistats/2005/hein2005aistats-hilbertian/}
}