  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.
