We introduce a new algorithm, called the swapping algorithm, to approximate numerically the minimal and maximal expected inner product of two random vectors with given marginal distributions. As a direct application, the algorithm computes an approximation of the L2-Wasserstein distance between two multivariate measures. The algorithm is simple to implement, accurate and less computationally expensive than the algorithms generally used in the literature for this problem. The algorithm also provides a discretized image of optimal measures and can be extended to more general cost functionals.

An algorithm to approximate the optimal expected inner product of two vectors with given marginals / G. Puccetti. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 451(2017), pp. 132-145. [10.1016/j.jmaa.2017.02.003]

### An algorithm to approximate the optimal expected inner product of two vectors with given marginals

#### Abstract

We introduce a new algorithm, called the swapping algorithm, to approximate numerically the minimal and maximal expected inner product of two random vectors with given marginal distributions. As a direct application, the algorithm computes an approximation of the L2-Wasserstein distance between two multivariate measures. The algorithm is simple to implement, accurate and less computationally expensive than the algorithms generally used in the literature for this problem. The algorithm also provides a discretized image of optimal measures and can be extended to more general cost functionals.
##### Scheda breve Scheda completa Scheda completa (DC)
Earth Mover's Distance; Linear Sum Assignment Problem; Optimal transportations; p-Wasserstein distance; Swapping algorithm; Analysis; Applied Mathematics
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore SECS-S/01 - Statistica
Settore MAT/06 - Probabilita' e Statistica Matematica
2017
http://dx.doi.org/10.1016/j.jmaa.2017.02.003
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/482991`