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Hilbertian Metrics and Positive Definite Kernels on Probability Measures


Conference Paper


We investigate the problem of defining Hilbertian metrics resp. positive definite kernels on probability measures, continuing previous work. This type of kernels has shown very good results in text classification and has a wide range of possible applications. In this paper we extend the two-parameter family of Hilbertian metrics of Topsoe such that it now includes all commonly used Hilbertian metrics on probability measures. This allows us to do model selection among these metrics in an elegant and unified way. Second we investigate further our approach to incorporate similarity information of the probability space into the kernel. The analysis provides a better understanding of these kernels and gives in some cases a more efficient way to compute them. Finally we compare all proposed kernels in two text and two image classification problems.

Author(s): Hein, M. and Bousquet, O.
Book Title: AISTATS 2005
Journal: Proceedings of AISTATS 2005
Pages: 136-143
Year: 2005
Month: January
Day: 0
Editors: Cowell, R. , Z. Ghahramani

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: Tenth International Workshop on Artificial Intelligence and Statistics (AI & Statistics 2005)
Event Place: Barbados

Digital: 0
ISBN: 0-9727358-1-X
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {Hilbertian Metrics and Positive Definite Kernels on Probability Measures},
  author = {Hein, M. and Bousquet, O.},
  journal = {Proceedings of AISTATS 2005},
  booktitle = {AISTATS 2005},
  pages = {136-143},
  editors = {Cowell, R. , Z. Ghahramani},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = jan,
  year = {2005},
  month_numeric = {1}