We study simultaneous inference for multiple matrix-variate Gaussian graphical models in high-dimensional settings. Such models arise when spatiotemporal data are collected across multiple sample groups or experimental sessions, where each group is characterized by its own graphical structure but shares common sparsity patterns. A central challenge is to conduct valid inference on collections of graph edges while efficiently borrowing strength across groups under both high-dimensionality and temporal dependence. We propose a unified framework that combines joint estimation via group penalized regression with a high-dimensional Gaussian approximation bootstrap to enable global testing of edge subsets of arbitrary size. The proposed procedure accommodates temporally dependent observations and avoids naive pooling across heterogeneous groups. We establish theoretical guarantees for the validity of the simultaneous tests under mild conditions on sample size, dimensionality, and non-stationary autoregressive temporal dependence, and show that the resulting tests are nearly optimal in terms of the testable region boundary. The method relies only on convex optimization and parametric bootstrap, making it computationally tractable. Simulation studies and a neural recording example illustrate the efficacy of the proposed approach.

翻译：本研究探讨高维环境下多矩阵变量高斯图模型的同步推断问题。此类模型适用于跨多个样本组或实验会话收集的时空数据，其中每组数据具有其独特的图结构，但共享共同的稀疏模式。核心挑战在于：在高维性和时间依赖性的双重约束下，对图边集合进行有效推断的同时，实现跨组别的信息高效共享。我们提出一个统一框架，该框架通过组惩罚回归进行联合估计，并结合高维高斯近似自举法，从而实现对任意规模边子集的全局检验。所提出的方法能够处理时间依赖的观测数据，并避免对异质组别进行简单合并。我们在样本量、维度和非平稳自回归时间依赖性的温和条件下，为同步检验的有效性建立了理论保证，并证明所得检验在可检验区域边界方面接近最优。该方法仅依赖于凸优化和参数自举，具有计算可行性。模拟研究和神经记录实例验证了所提方法的有效性。