Efficient Alternating Minimization Solvers for Wyner Multi-View Unsupervised Learning

Abstract: In this work, we adopt Wyner common information framework for unsupervised multi-view representation learning. Within this framework, we propose two novel formulations that enable the development of computational efficient solvers based on the alternating minimization principle. The first formulation, referred to as the {\em variational form}, enjoys a linearly growing complexity with the number of views and is based on a variational-inference tight surrogate bound coupled with a Lagrangian optimization objective function. The second formulation, i.e., the {\em representational form}, is shown to include known results as special cases. Here, we develop a tailored version from the alternating direction method of multipliers (ADMM) algorithm for solving the resulting non-convex optimization problem. In the two cases, the convergence of the proposed solvers is established in certain relevant regimes. Furthermore, our empirical results demonstrate the effectiveness of the proposed methods as compared with the state-of-the-art solvers. In a nutshell, the proposed solvers offer computational efficiency, theoretical convergence guarantees (local minima), scalable complexity with the number of views, and exceptional accuracy as compared with the state-of-the-art techniques. Our focus here is devoted to the discrete case and our results for continuous distributions are reported elsewhere.