Probabilistic Partial Canonical Correlation Analysis

Yusuke Mukuta,  Harada
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):1449-1457, 2014.

Abstract

Partial canonical correlation analysis (partial CCA) is a statistical method that estimates a pair of linear projections onto a low dimensional space, where the correlation between two multidimensional variables is maximized after eliminating the influence of a third variable. Partial CCA is known to be closely related to a causality measure between two time series. However, partial CCA requires the inverses of covariance matrices, so the calculation is not stable. This is particularly the case for high-dimensional data or small sample sizes. Additionally, we cannot estimate the optimal dimension of the subspace in the model. In this paper, we have addressed these problems by proposing a probabilistic interpretation of partial CCA and deriving a Bayesian estimation method based on the probabilistic model. Our numerical experiments demonstrated that our methods can stably estimate the model parameters, even in high dimensions or when there are a small number of samples.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-mukuta14, title = {Probabilistic Partial Canonical Correlation Analysis}, author = {Mukuta, Yusuke and Harada, }, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {1449--1457}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/mukuta14.pdf}, url = {https://proceedings.mlr.press/v32/mukuta14.html}, abstract = {Partial canonical correlation analysis (partial CCA) is a statistical method that estimates a pair of linear projections onto a low dimensional space, where the correlation between two multidimensional variables is maximized after eliminating the influence of a third variable. Partial CCA is known to be closely related to a causality measure between two time series. However, partial CCA requires the inverses of covariance matrices, so the calculation is not stable. This is particularly the case for high-dimensional data or small sample sizes. Additionally, we cannot estimate the optimal dimension of the subspace in the model. In this paper, we have addressed these problems by proposing a probabilistic interpretation of partial CCA and deriving a Bayesian estimation method based on the probabilistic model. Our numerical experiments demonstrated that our methods can stably estimate the model parameters, even in high dimensions or when there are a small number of samples.} }
Endnote
%0 Conference Paper %T Probabilistic Partial Canonical Correlation Analysis %A Yusuke Mukuta %A Harada %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-mukuta14 %I PMLR %P 1449--1457 %U https://proceedings.mlr.press/v32/mukuta14.html %V 32 %N 2 %X Partial canonical correlation analysis (partial CCA) is a statistical method that estimates a pair of linear projections onto a low dimensional space, where the correlation between two multidimensional variables is maximized after eliminating the influence of a third variable. Partial CCA is known to be closely related to a causality measure between two time series. However, partial CCA requires the inverses of covariance matrices, so the calculation is not stable. This is particularly the case for high-dimensional data or small sample sizes. Additionally, we cannot estimate the optimal dimension of the subspace in the model. In this paper, we have addressed these problems by proposing a probabilistic interpretation of partial CCA and deriving a Bayesian estimation method based on the probabilistic model. Our numerical experiments demonstrated that our methods can stably estimate the model parameters, even in high dimensions or when there are a small number of samples.
RIS
TY - CPAPER TI - Probabilistic Partial Canonical Correlation Analysis AU - Yusuke Mukuta AU - Harada BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-mukuta14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 1449 EP - 1457 L1 - http://proceedings.mlr.press/v32/mukuta14.pdf UR - https://proceedings.mlr.press/v32/mukuta14.html AB - Partial canonical correlation analysis (partial CCA) is a statistical method that estimates a pair of linear projections onto a low dimensional space, where the correlation between two multidimensional variables is maximized after eliminating the influence of a third variable. Partial CCA is known to be closely related to a causality measure between two time series. However, partial CCA requires the inverses of covariance matrices, so the calculation is not stable. This is particularly the case for high-dimensional data or small sample sizes. Additionally, we cannot estimate the optimal dimension of the subspace in the model. In this paper, we have addressed these problems by proposing a probabilistic interpretation of partial CCA and deriving a Bayesian estimation method based on the probabilistic model. Our numerical experiments demonstrated that our methods can stably estimate the model parameters, even in high dimensions or when there are a small number of samples. ER -
APA
Mukuta, Y. & Harada, . (2014). Probabilistic Partial Canonical Correlation Analysis. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):1449-1457 Available from https://proceedings.mlr.press/v32/mukuta14.html.

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