Tensor Analyzers

Yichuan Tang, Ruslan Salakhutdinov, Geoffrey Hinton
Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):163-171, 2013.

Abstract

Factor Analysis is a statistical method that seeks to explain linear variations in data by using unobserved latent variables. Due to its additive nature, it is not suitable for modeling data that is generated by multiple groups of latent factors which interact multiplicatively. In this paper, we introduce Tensor Analyzers which are a multilinear generalization of Factor Analyzers. We describe an efficient way of sampling from the posterior distribution over factor values and we demonstrate that these samples can be used in the EM algorithm for learning interesting mixture models of natural image patches. Tensor Analyzers can also accurately recognize a face under significant pose and illumination variations when given only one previous image of that face. We also show that Tensor Analyzers can be trained in an unsupervised, semi-supervised, or fully supervised settings.

Cite this Paper

BibTeX
@InProceedings{pmlr-v28-tang13, title = {Tensor Analyzers}, author = {Tang, Yichuan and Salakhutdinov, Ruslan and Hinton, Geoffrey}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {163--171}, year = {2013}, editor = {Dasgupta, Sanjoy and McAllester, David}, volume = {28}, number = {3}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/tang13.pdf}, url = {https://proceedings.mlr.press/v28/tang13.html}, abstract = {Factor Analysis is a statistical method that seeks to explain linear variations in data by using unobserved latent variables. Due to its additive nature, it is not suitable for modeling data that is generated by multiple groups of latent factors which interact multiplicatively. In this paper, we introduce Tensor Analyzers which are a multilinear generalization of Factor Analyzers. We describe an efficient way of sampling from the posterior distribution over factor values and we demonstrate that these samples can be used in the EM algorithm for learning interesting mixture models of natural image patches. Tensor Analyzers can also accurately recognize a face under significant pose and illumination variations when given only one previous image of that face. We also show that Tensor Analyzers can be trained in an unsupervised, semi-supervised, or fully supervised settings.} }
Endnote
%0 Conference Paper %T Tensor Analyzers %A Yichuan Tang %A Ruslan Salakhutdinov %A Geoffrey Hinton %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-tang13 %I PMLR %P 163--171 %U https://proceedings.mlr.press/v28/tang13.html %V 28 %N 3 %X Factor Analysis is a statistical method that seeks to explain linear variations in data by using unobserved latent variables. Due to its additive nature, it is not suitable for modeling data that is generated by multiple groups of latent factors which interact multiplicatively. In this paper, we introduce Tensor Analyzers which are a multilinear generalization of Factor Analyzers. We describe an efficient way of sampling from the posterior distribution over factor values and we demonstrate that these samples can be used in the EM algorithm for learning interesting mixture models of natural image patches. Tensor Analyzers can also accurately recognize a face under significant pose and illumination variations when given only one previous image of that face. We also show that Tensor Analyzers can be trained in an unsupervised, semi-supervised, or fully supervised settings.
RIS
TY - CPAPER TI - Tensor Analyzers AU - Yichuan Tang AU - Ruslan Salakhutdinov AU - Geoffrey Hinton BT - Proceedings of the 30th International Conference on Machine Learning DA - 2013/05/26 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-tang13 PB - PMLR DP - Proceedings of Machine Learning Research VL - 28 IS - 3 SP - 163 EP - 171 L1 - http://proceedings.mlr.press/v28/tang13.pdf UR - https://proceedings.mlr.press/v28/tang13.html AB - Factor Analysis is a statistical method that seeks to explain linear variations in data by using unobserved latent variables. Due to its additive nature, it is not suitable for modeling data that is generated by multiple groups of latent factors which interact multiplicatively. In this paper, we introduce Tensor Analyzers which are a multilinear generalization of Factor Analyzers. We describe an efficient way of sampling from the posterior distribution over factor values and we demonstrate that these samples can be used in the EM algorithm for learning interesting mixture models of natural image patches. Tensor Analyzers can also accurately recognize a face under significant pose and illumination variations when given only one previous image of that face. We also show that Tensor Analyzers can be trained in an unsupervised, semi-supervised, or fully supervised settings. ER -
APA
Tang, Y., Salakhutdinov, R. & Hinton, G.. (2013). Tensor Analyzers. Proceedings of the 30th International Conference on Machine Learning, in Proceedings of Machine Learning Research 28(3):163-171 Available from https://proceedings.mlr.press/v28/tang13.html.

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