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Integral Probability Metrics and Their Generating Classes of Functions
Abstract
We consider probability metrics of the following type: for a class of functions and probability measures P, Q we define A unified study of such integral probability metrics is given. We characterize the maximal class of functions that generates such a metric. Further, we show how some interesting properties of these probability metrics arise directly from conditions on the generating class of functions. The results are illustrated by several examples, including the Kolmogorov metric, the Dudley metric and the stop-loss metric.
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Cited by
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Distributional Reinforcement Learning With Quantile Regression
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Equivalence of distance-based and RKHS-based statistics in hypothesis testing
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Metadata
- Authors
- Müller, A.
- Venue
- Advances in Applied Probability
- Publisher
- Cambridge University Press
- Published
- 1997-06-01
- Volume
- 29
- Issue
- 02
- Pages
- 429-443
- ISSN
- 0001-8678 (ISSN-L)
- OpenAlex
- W2328111639
- Cited by
- 548
- References
- 0
- FWCI
- 0.43
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
