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.
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Muñoz, A., Martos, G., Arriero, J., Gonzalez, J. (2012). A New Distance for Probability Measures Based on the Estimation of Level Sets. In: Villa, A.E.P., Duch, W., Érdi, P., Masulli, F., Palm, G. (eds) Artificial Neural Networks and Machine Learning – ICANN 2012. ICANN 2012. Lecture Notes in Computer Science, vol 7553. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33266-1_34
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DOI: https://doi.org/10.1007/978-3-642-33266-1_34
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