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, 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：本研究采用Wyner公共信息框架进行无监督多视图表示学习。在该框架下，我们提出两种新公式，使得能够基于交替最小化原则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，基于变分推理的紧代理界与拉格朗日优化目标函数相结合。第二种公式即表示形式，被证明包含已知结果作为特例。在此，我们针对产生的非凸优化问题，开发了交替方向乘子法（ADMM）算法的定制版本。在两种情况下，我们证明了所提求解器在相关条件下的收敛性。此外，实验结果展示了所提方法相较于最先进求解器的有效性。总而言之，所提求解器具有计算效率高、理论收敛保证、复杂度随视图数量可扩展以及相较于最先进技术精度卓越的特点。本文侧重离散情况，连续分布的结果将另行报道。