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.

翻译：在本文中，我们采用Wyner共同信息框架进行无监督多视图表示学习。在该框架下，我们提出两种新颖的公式，使得能够基于交替最小化原理开发计算高效的求解器。第一种公式称为“变分形式”，其复杂度随视图数量线性增长，基于变分推理的紧致代理界与拉格朗日优化目标函数相结合。第二种公式称为“表示形式”，被证明囊括了已知结果作为特例。在此，我们针对由此产生的非凸优化问题，开发了一种专门定制的交替方向乘子法（ADMM）算法求解器。在这两种情况下，我们证明了所提求解器在相关特定条件下的收敛性。此外，我们的实验结果表明，与最先进的求解器相比，所提方法具有有效性。简而言之，所提求解器提供了计算效率、理论收敛性保证（局部极小值）、随视图数量可扩展的复杂度，以及与最先进技术相比卓越的准确性。本文重点关注离散情况，连续分布的结果将在另文报告。