发表机构
Univ. Grenoble Alpes; CNRS; Grenoble INP; Inria; LJK; G-SCOP（格勒诺布尔阿尔卑斯大学; 国家科学研究中心; 格勒诺布尔研究所; 法国国家信息与自动化技术研究院; 实验室; G-SCOP研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究基于图结构生成规定稀疏模式的相关矩阵，提出凸优化框架，通过投影初始矩阵到椭圆体实现。该方法比现有方法灵活，能控制非对角元素分布均值，生成适用于基准测试的矩阵，还应用于真实数据集并与GAN方法比较。
AI 中文摘要
这项工作致力于生成与图结构相关的具有规定稀疏模式的理论相关矩阵。我们提出了一种新颖的凸优化框架，在半正定约束下将初始矩阵投影到椭圆体上。实施并比较了几种数值方案。该问题属于矩阵补全的更广泛类别，对应缺失边的非对角元素固定为零，对角元素固定为一。除了这种结构约束，该方法通过允许控制非对角元素分布的均值，比现有方法具有更大的灵活性，能够生成更好反映现实数据的相关矩阵。此过程并非旨在在可行集上产生均匀分布，而是提供了一种有原则且可调整的方式来构建适用于图形模型推断统计方法基准测试的相关矩阵。在一般情况下以及额外均值约束下都建立了解的存在性理论保证。模拟研究说明了生成矩阵相对于图结构的性质。该方法应用于神经科学和金融的两个真实世界数据集，并与基于GAN的相关矩阵生成进行了比较。
英文摘要
This work addresses the generation of theoretical correlation matrices with prescribed sparsity patterns associated to graph structures. We propose a novel convex optimization framework in which an initial matrix is projected onto an elliptope under a positive semidefiniteness constraint. Several numerical schemes are implemented and compared. The problem falls within the broader class of matrix completion, where off-diagonal entries corresponding to absent edges are fixed to zero and diagonal entries are fixed to one. Beyond this structural constraint, the approach offers greater flexibility than existing methods by allowing control over the mean of the off-diagonal entry distribution, enabling the generation of correlation matrices that better reflect realistic data. This procedure is not designed to yield a uniform distribution over the feasible set; rather, it provides a principled and tunable way to construct correlation matrices suitable for benchmarking statistical methods for graphical model inference. Theoretical guarantees on the existence of solutions are established, both in the general setting and under the additional mean constraint. Simulation studies illustrate the properties of the generated matrices with respect to graph structure. The methodology is applied to two real-world datasets from neuroscience and finance, and a comparison with GAN-based correlation matrix generation is provided.
