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1 LIENS - Laboratoire d-informatique de l-école normale supérieure 2 MSR - INRIA - Microsoft Research - Inria Joint Centre 3 SIERRA - Statistical Machine Learning and Parsimony DI-ENS - Département d-informatique de l-École normale supérieure, ENS Paris - École normale supérieure - Paris, CNRS - Centre National de la Recherche Scientifique, Inria de Paris 4 DI-ENS - Département d-informatique de l-École normale supérieure

Abstract : We introduce three novel semi-parametric extensions of probabilistic canonical correlation analysis with identifiability guarantees. We consider moment matching techniques for estimation in these models. For that, by drawing explicit links between the new models and a discrete version of independent component analysis DICA, we first extend the DICA cumulant tensors to the new discrete version of CCA. By further using a close connection with independent component analysis, we introduce generalized covariance matrices , which can replace the cumulant tensors in the moment matching framework, and, therefore, improve sample complexity and simplify derivations and algorithms significantly. As the tensor power method or orthogonal joint diagonalization are not applicable in the new setting, we use non-orthogonal joint diago-nalization techniques for matching the cumulants. We demonstrate performance of the proposed models and estimation techniques on experiments with both synthetic and real datasets.





Author: Anastasia Podosinnikova - Francis Bach - Simon Lacoste-Julien -

Source: https://hal.archives-ouvertes.fr/



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