A contribution to Optimal Transport on incomparable spaces
作者： Titouan Vayer
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摘要: Le Transport Optimal est une theorie permettant de definir des notions geometriques distance entre distributions probabilite et trouver correspondances, relations, ensembles points. De cette theorie, a la frontiere les mathematiques l'optimisation, decoule nombreuses applications en machine learning. Cette these propose d'etudier le scenario, complexe, dans lequel differentes donnees appartiennent espaces incomparables}. En particulier nous abordons questions suivantes : comment appliquer transport optimal graphes, structurees ? Comment l'adapter lorsque sont variees ne font pas partie d'un meme espace metrique un ensemble d'outils pour ces differents cas. Un important volet notamment consacre l'etude Gromov-Wasserstein dont proprietes permettent d'interessants problemes sur incomparables. Plus largement, analysons outils proposes, etablissons solutions algorithmiques calculer etudions leur applicabilite nombreux scenarii learning qui couvrent, notamment, classification, simplification, partitionnement structurees, ainsi que l'adaptation domaines heterogenes.
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