Probabilistic CCA with Implicit Distributions

Abstract

Canonical Correlation Analysis (CCA) is a classic technique for multi-view data analysis. To overcome the deficiency of linear correlation in practical multi-view learning tasks, various CCA variants were proposed to capture nonlinear dependency. However, it is non-trivial to have an in-principle understanding of these variants due to their inherent restrictive assumption on the data and latent code distributions. Although some works have studied probabilistic interpretation for CCA, these models still require the explicit form of the distributions to achieve a tractable solution for the inference. In this work, we study probabilistic interpretation for CCA based on implicit distributions. We present Conditional Mutual Information (CMI) as a new criterion for CCA to consider both linear and nonlinear dependency for arbitrarily distributed data. To eliminate direct estimation for CMI, in which explicit form of the distributions is still required, we derive an objective which can provide an estimation for CMI with efficient inference methods. To facilitate Bayesian inference of multi-view analysis, we propose Adversarial CCA (ACCA), which achieves consistent encoding for multiview data with the consistent constraint imposed on the marginalization of the implicit posteriors. Such a model would achieve superiority in the alignment of the multi-view data with implicit distributions. It is interesting to note that most of the existing CCA variants can be connected with our proposed CCA model by assigning specific form for the posterior and likelihood distributions. Extensive experiments on nonlinear † indicates the corresponding author.