A new distance for probability measures based on the estimation of level sets

Authors:
Alberto Muñoz;Gabriel Martos;Javier Arriero;Javier Gonzalez
Affiliations:
Department of Statistics, University Carlos III, Madrid, Spain;Department of Statistics, University Carlos III, Madrid, Spain;Department of Statistics, University Carlos III, Madrid, Spain;Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, The Netherlands
Venue:
ICANN'12 Proceedings of the 22nd international conference on Artificial Neural Networks and Machine Learning - Volume Part II
Year:
2012

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Abstract

In this paper we propose to consider Probability Measures (PM) as generalized functions belonging to some functional space endowed with an inner product. This approach allows to introduce a new family of distances for PMs. We propose a particular (non parametric) metric for PMs belonging to this class, based on the estimation of density level sets. Some real and simulated data sets are used for a first exploration of its performance.