Multiple Operator-valued Kernel Learning
By Hachem Kadri, Alain Rakotomamonjy, Francis R. Bach, Philippe Preux. 2012
19 citations recorded by the source corpus.
Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of infinite-dimensional operator-valued kernels which are suitable for extending functional data analysis methods to nonlinear contexts. We study this problem in the case of kernel ridge regression for functional responses with an lr-norm constraint on the combination coefficients (r ≥ 1). The resulting optimization problem is more involved than those of multiple scalar-valued kernel learning since operator-valued kernels pose more technical and theoretical issues. We propose a multiple operator-valued kernel learning algorithm based on solving a system of linear operator equations by using a block coordinate-descent procedure. We experimentally validate our approach on a functional regression task in the context of finger movement prediction in brain-computer interfaces.
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- Bharath K. Sriperumbudur
- Krikamol Muandet
- Arthur Gretton
- Barnab'as P'oczos
- Bernhard Schölkopf
- Zoltán Szabó
- Kenji Fukumizu
- David Lopez-Paz
Citations in the corpus
- Learning Theory for Distribution Regression (2014, background): “, 2013), finger trajectory prediction in brain-computer interfaces (Kadri et al., 2012) or ecological inference (Flaxman et al.”
- Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality (2012, background): “This is in contrast to recent efforts [12, 18] where only one of the two components is optimized, and the full complexity of the joint problem is not addressed.”
- Operator-valued Kernels for Learning from Functional Response Data (2015, background): “Recent works in this direction includes the papers of Dinuzzo et al. (2011), Kadri et al. (2012), Sindhwani et al. (2013) and Lim et al. (2015), but further investigations are needed in this area.”