Canonical Correlation Analysis (CCA) is a statistical technique used to extract common information from multiple data sources or views. It has been used in various representation learning problems, such as dimensionality reduction, word embedding, and clustering. Recent work has given CCA probabilistic footing in a deep learning context and uses a variational lower bound for the data log likelihood to estimate model parameters. Alternatively, adversarial techniques have arisen in recent years as a powerful alternative to variational Bayesian methods in autoencoders. In this work, we explore straightforward adversarial alternatives to recent work in Deep Variational CCA (VCCA and VCCA-Private) we call ACCA and ACCA-Private and show how these approaches offer a stronger and more flexible way to match the approximate posteriors coming from encoders to much larger classes of priors than the VCCA and VCCA-Private models. This allows new priors for what constitutes a good representation, such as disentangling underlying factors of variation, to be more directly pursued. We offer further analysis on the multi-level disentangling properties of VCCA-Private and ACCA-Private through the use of a newly designed dataset we call Tangled MNIST. We also design a validation criteria for these models that is theoretically grounded, task-agnostic, and works well in practice. Lastly, we fill a minor research gap by deriving an additional variational lower bound for VCCA that allows the representation to use view-specific information from both input views.
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