Beyond CCA: Moment Matching for Multi-View Models
By Anastasia Podosinnikova, Francis R. Bach, Simon Lacoste-Julien. 2016
16 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Representation & Self-Supervised Learning, Signal Processing
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Citations in the corpus
- Multi-omic and multi-view clustering algorithms: review and cancer benchmark (2018, background): “Finally, [43] extended CCA to support count data, which are common in biological datasets.”
- Multi-Task Clustering with Model Relation Learning (2018, methodology): “Canonical correlation analysis [Hotelling, 1936; Podosinnikova et al. , 2016 ] aims to find the linear projections which have maximum correlation among different views.”
- Multi-view learning overview: Recent progress and new challenges (2017, methodology): “In addition, some extensions of probabilistic CCA models have been provided as non-Gaussian CCA, discrete CCA and mixed CCA which were adapted to applications where one or both of the data-views are either counts [82].”