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Empirical Inference Conference Paper 2011

Learning low-rank output kernels

Thumb ticker sm francesco dinuzzo
Empirical Inference
Francesco Dinuzzo
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Empirical Inference
Kenji Fukumizu

Output kernel learning techniques allow to simultaneously learn a vector-valued function and a positive semidefinite matrix which describes the relationships between the outputs. In this paper, we introduce a new formulation that imposes a low-rank constraint on the output kernel and operates directly on a factor of the kernel matrix. First, we investigate the connection between output kernel learning and a regularization problem for an architecture with two layers. Then, we show that a variety of methods such as nuclear norm regularized regression, reduced-rank regression, principal component analysis, and low rank matrix approximation can be seen as special cases of the output kernel learning framework. Finally, we introduce a block coordinate descent strategy for learning low-rank output kernels.

Author(s): Dinuzzo, F. and Fukumizu, K.
Book Title: JMLR Workshop and Conference Proceedings Volume 20
Pages: 181-196
Year: 2011
Month: November
Day: 0
Editors: Hsu, C.-N. , W.S. Lee
Publisher: JMLR
Bibtex Type: Conference Paper (inproceedings)
Address: Cambridge, MA, USA
Event Name: 3rd Asian Conference on Machine Learning (ACML 2011)
Event Place: Taoyuan, Taiwan
Digital: 0
Electronic Archiving: grant_archive
Links:

BibTex 

@inproceedings{DinuzzoF2011,
  title = {Learning low-rank output kernels},
  booktitle = {JMLR Workshop and Conference Proceedings Volume 20},
  abstract = {Output kernel learning techniques allow to simultaneously learn a vector-valued function and a positive semidefinite matrix which describes the relationships between the outputs. In this paper, we introduce a new formulation that imposes a low-rank constraint on the output kernel and operates directly on a factor of the kernel matrix. First, we investigate the connection between output kernel learning and a regularization problem for an architecture
  with two layers. Then, we show that a variety of methods such as nuclear norm regularized regression, reduced-rank regression, principal component analysis, and low rank matrix approximation can be seen as special cases of the output kernel learning framework. Finally, we introduce a block coordinate descent strategy for learning low-rank output kernels.},
  pages = {181-196},
  editors = {Hsu, C.-N. , W.S. Lee},
  publisher = {JMLR},
  address = {Cambridge, MA, USA},
  month = nov,
  year = {2011},
  slug = {dinuzzof2011},
  author = {Dinuzzo, F. and Fukumizu, K.},
  month_numeric = {11}
}