Advances in spatial transcriptomics (ST) technologies enable systematic molecular characterization of tumor microenvironment, tumor gradients and gene regulatory networks. Cancer progression is known to vary along pathological gradients, yet existing network approaches for gene network inference typically ignore hierarchical spatial organization across the tumor. We develop a Bayesian multi-resolution spatial graphical regression (mSGR) framework to infer spatially varying gene networks from multi-resolution ST data. The proposed model allows precision matrices to vary across hierarchically structured spatial domains, capturing both local and global organization within the tumor. To identify spatially varying regulatory relationships, we introduce a spatially structured edge selection strategy that borrows strength across regions according to spatial proximity and pathological gradients, while Gaussian-process priors flexibly model spatial variation in edge strengths. Scalable inference is achieved through an augmented mean-field variational Bayes algorithm with node-wise parallel regressions, enabling efficient estimation in high-dimensional settings. Simulation studies demonstrate improved recovery of network structures compared with competing approaches. Applying mSGR to multi-resolution ST data from kidney cancer reveals stronger regulatory connectivity in transitional regions of epithelial-mesenchymal transition pathway and identifies hub genes along the tumor gradient, illustrating how spatially resolved network analysis can provide key insights into tumor microenvironment organization.

翻译：空间转录组学（ST）技术的进步使得能够系统性地对肿瘤微环境、肿瘤梯度及基因调控网络进行分子表征。已知肿瘤进展沿病理梯度变化，然而现有用于基因网络推断的网络方法通常忽略了跨肿瘤的分层空间组织。我们开发了一个贝叶斯多分辨率空间图回归（mSGR）框架，用于从多分辨率ST数据中推断空间变化的基因网络。所提出的模型允许精度矩阵跨分层结构的空间区域变化，捕捉肿瘤内的局部和全局组织。为识别空间变化的调控关系，我们引入了一种空间结构化的边选择策略，该策略根据空间邻近性和病理梯度跨区域借用统计强度，同时高斯过程先验灵活地建模边强度的空间变化。通过一种带节点级并行回归的增广均值场变分贝叶斯算法实现可扩展推断，从而在高维场景下实现高效估计。模拟研究表明，与竞争方法相比，该方法能更有效地恢复网络结构。将mSGR应用于肾癌的多分辨率ST数据，揭示了上皮-间充质转化通路过渡区域中更强的调控连接性，并识别了沿肿瘤梯度的枢纽基因，阐明了空间分辨网络分析如何为肿瘤微环境组织提供关键见解。