Wasserstein Distance Measure Machines

Abstract : This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of distributions to some reference distributions denoted as templates. Our framework extends the theory of similarity of \citet{balcan2008theory} to the population distribution case and we prove that, for some learning problems, Wasserstein distance achieves low-error linear decision functions with high probability. Our key result is to prove that the theory also holds for empirical distributions. Algorithmically, the proposed approach is very simple as it consists in computing a mapping based on pairwise Wasserstein distances and then learning a linear decision function. Our experimental results show that this Wasserstein distance embedding performs better than kernel mean embeddings and computing Wasserstein distance is far more tractable than estimating pairwise Kullback-Leibler divergence of empirical distributions.
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01717940
Contributeur : Alain Rakotomamonjy <>
Soumis le : mardi 27 février 2018 - 22:09:10
Dernière modification le : mardi 5 juin 2018 - 10:14:25
Document(s) archivé(s) le : lundi 28 mai 2018 - 18:30:45

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WDMM.pdf
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  • HAL Id : hal-01717940, version 1
  • ARXIV : 1803.00250

Citation

Alain Rakotomamonjy, Abraham Traore, Maxime Berar, Rémi Flamary, Nicolas Courty. Wasserstein Distance Measure Machines. 2018. 〈hal-01717940〉

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