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Probabilistic Partial Canonical Correlation Analysis
Authors: Yusuke Mukuta and Tatsuya Harada
Conference: Proceedings of the 31st International Conference on Machine Learning (ICML-14)
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.
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