Factorized Orthogonal Latent Spaces

Mathieu Salzmann, Carl Henrik Ek, Raquel Urtasun, Trevor Darrell
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:701-708, 2010.

Abstract

Existing approaches to multi-view learning are particularly effective when the views are either independent (i.e, multi-kernel approaches) or fully dependent (i.e., shared latent spaces). However, in real scenarios, these assumptions are almost never truly satisfied. Recently, two methods have attempted to tackle this problem by factorizing the information and learn separate latent spaces for modeling the shared (i.e., correlated) and private (i.e., independent) parts of the data. However, these approaches are very sensitive to parameters setting or initialization. In this paper we propose a robust approach to factorizing the latent space into shared and private spaces by introducing orthogonality constraints, which penalize redundant latent representations. Furthermore, unlike previous approaches, we simultaneously learn the structure and dimensionality of the latent spaces by relying on a regularizer that encourages the latent space of each data stream to be low dimensional. To demonstrate the benefits of our approach, we apply it to two existing shared latent space models that assume full dependence of the views, the sGPLVM and the sKIE, and show that our constraints improve the performance of these models on the task of pose estimation from monocular images.

Cite this Paper


BibTeX
@InProceedings{pmlr-v9-salzmann10a, title = {Factorized Orthogonal Latent Spaces}, author = {Salzmann, Mathieu and Ek, Carl Henrik and Urtasun, Raquel and Darrell, Trevor}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {701--708}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/salzmann10a/salzmann10a.pdf}, url = { http://proceedings.mlr.press/v9/salzmann10a.html }, abstract = {Existing approaches to multi-view learning are particularly effective when the views are either independent (i.e, multi-kernel approaches) or fully dependent (i.e., shared latent spaces). However, in real scenarios, these assumptions are almost never truly satisfied. Recently, two methods have attempted to tackle this problem by factorizing the information and learn separate latent spaces for modeling the shared (i.e., correlated) and private (i.e., independent) parts of the data. However, these approaches are very sensitive to parameters setting or initialization. In this paper we propose a robust approach to factorizing the latent space into shared and private spaces by introducing orthogonality constraints, which penalize redundant latent representations. Furthermore, unlike previous approaches, we simultaneously learn the structure and dimensionality of the latent spaces by relying on a regularizer that encourages the latent space of each data stream to be low dimensional. To demonstrate the benefits of our approach, we apply it to two existing shared latent space models that assume full dependence of the views, the sGPLVM and the sKIE, and show that our constraints improve the performance of these models on the task of pose estimation from monocular images.} }
Endnote
%0 Conference Paper %T Factorized Orthogonal Latent Spaces %A Mathieu Salzmann %A Carl Henrik Ek %A Raquel Urtasun %A Trevor Darrell %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-salzmann10a %I PMLR %P 701--708 %U http://proceedings.mlr.press/v9/salzmann10a.html %V 9 %X Existing approaches to multi-view learning are particularly effective when the views are either independent (i.e, multi-kernel approaches) or fully dependent (i.e., shared latent spaces). However, in real scenarios, these assumptions are almost never truly satisfied. Recently, two methods have attempted to tackle this problem by factorizing the information and learn separate latent spaces for modeling the shared (i.e., correlated) and private (i.e., independent) parts of the data. However, these approaches are very sensitive to parameters setting or initialization. In this paper we propose a robust approach to factorizing the latent space into shared and private spaces by introducing orthogonality constraints, which penalize redundant latent representations. Furthermore, unlike previous approaches, we simultaneously learn the structure and dimensionality of the latent spaces by relying on a regularizer that encourages the latent space of each data stream to be low dimensional. To demonstrate the benefits of our approach, we apply it to two existing shared latent space models that assume full dependence of the views, the sGPLVM and the sKIE, and show that our constraints improve the performance of these models on the task of pose estimation from monocular images.
RIS
TY - CPAPER TI - Factorized Orthogonal Latent Spaces AU - Mathieu Salzmann AU - Carl Henrik Ek AU - Raquel Urtasun AU - Trevor Darrell BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-salzmann10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 701 EP - 708 L1 - http://proceedings.mlr.press/v9/salzmann10a/salzmann10a.pdf UR - http://proceedings.mlr.press/v9/salzmann10a.html AB - Existing approaches to multi-view learning are particularly effective when the views are either independent (i.e, multi-kernel approaches) or fully dependent (i.e., shared latent spaces). However, in real scenarios, these assumptions are almost never truly satisfied. Recently, two methods have attempted to tackle this problem by factorizing the information and learn separate latent spaces for modeling the shared (i.e., correlated) and private (i.e., independent) parts of the data. However, these approaches are very sensitive to parameters setting or initialization. In this paper we propose a robust approach to factorizing the latent space into shared and private spaces by introducing orthogonality constraints, which penalize redundant latent representations. Furthermore, unlike previous approaches, we simultaneously learn the structure and dimensionality of the latent spaces by relying on a regularizer that encourages the latent space of each data stream to be low dimensional. To demonstrate the benefits of our approach, we apply it to two existing shared latent space models that assume full dependence of the views, the sGPLVM and the sKIE, and show that our constraints improve the performance of these models on the task of pose estimation from monocular images. ER -
APA
Salzmann, M., Ek, C.H., Urtasun, R. & Darrell, T.. (2010). Factorized Orthogonal Latent Spaces. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:701-708 Available from http://proceedings.mlr.press/v9/salzmann10a.html .

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