Multivariate Regression via Stiefel Manifold Constraints

BakIr, G; Gretton, A; Franz, M; Schölkopf, B

doi:10.1007/978-3-540-28649-3_32

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Multivariate Regression via Stiefel Manifold Constraints

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

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

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

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

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Citation

BakIr, G., Gretton, A., Franz, M., & Schölkopf, B. (2004). Multivariate Regression via Stiefel Manifold Constraints. In C. Rasmussen, H. Bülthoff, B. Schölkopf, & M. Giese (Eds.), Pattern Recognition: 26th DAGM Symposium, Tübingen, Germany, August 30 - September 1, 2004 (pp. 262-269). Berlin, Germany: Springer.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-F386-F

Abstract

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.