Beyond CCA: Moment Matching for Multi-View Models
This work addresses multi-view data analysis for researchers in machine learning, but it is incremental as it builds on existing CCA and ICA methods.
The authors introduced three semi-parametric extensions of probabilistic canonical correlation analysis with identifiability guarantees, using moment matching techniques for estimation, and demonstrated performance on synthetic and real datasets.
We introduce three novel semi-parametric extensions of probabilistic canonical correlation analysis with identifiability guarantees. We consider moment matching techniques for estimation in these models. For that, by drawing explicit links between the new models and a discrete version of independent component analysis (DICA), we first extend the DICA cumulant tensors to the new discrete version of CCA. By further using a close connection with independent component analysis, we introduce generalized covariance matrices, which can replace the cumulant tensors in the moment matching framework, and, therefore, improve sample complexity and simplify derivations and algorithms significantly. As the tensor power method or orthogonal joint diagonalization are not applicable in the new setting, we use non-orthogonal joint diagonalization techniques for matching the cumulants. We demonstrate performance of the proposed models and estimation techniques on experiments with both synthetic and real datasets.