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Multivariate Regression via Stiefel Manifold Constraints

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons83791

BakIr,  G
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83946

Gretton,  A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83919

Franz,  M
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zitation

BakIr, G., Gretton, A., Franz, M., & Schölkopf, B. (2004). Multivariate Regression via Stiefel Manifold Constraints. In DAGM 2004 (pp. 262-269). Berlin, Germany: Springer.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0013-F386-F
Zusammenfassung
We introduce a learning technique for regression between high-dimensional spaces. Standard methods typically reduce this task to many one-dimensional problems, with each output dimension considered independently. By contrast, in our approach the feature construction and the regression estimation are performed jointly, directly minimizing a loss function that we specify, subject to a rank constraint. A major advantage of this approach is that the loss is no longer chosen according to the algorithmic requirements, but can be tailored to the characteristics of the task at hand; the features will then be optimal with respect to this objective, and dependence between the outputs can be exploited.