Complex analyses involving multiple, dependent random quantities often lead to graphical models - a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical analyses for graphical data, especially towards generative modeling, one needs mathematical representations and metrics for matching and comparing graphs, and subsequent tools, such as geodesics, means, and covariances. This paper utilizes a quotient structure to develop efficient algorithms for computing these quantities, leading to useful statistical tools, including principal component analysis, statistical testing, and modeling. We demonstrate the efficacy of this framework using datasets taken from several problem areas, including letters, biochemical structures, and social networks.
Safe-Sora: Safe Text-to-Video Generation via Graphical Watermarking
Tsinghua University（清华大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；South China University of Technology（华南理工大学）；Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ)（广东人工智能与数字经济实验室）；Singapore Management University（新加坡管理学院）
MAM-E: Mammographic synthetic image generation with diffusion models
Computer Vision and Robotics Institute (ViCOROB), University of Girona（赫罗纳大学计算机视觉与机器人研究所（ViCOROB））；Clínica Girona, Institute of Diagnostic Imaging (IDI) Girona, University of Girona（赫罗纳大学赫罗纳诊所诊断影像研究所（IDI））
SpectralDiff: A Generative Framework for Hyperspectral Image Classification with Diffusion Models
Peking University（北京大学）；Central South University（中南大学）；Hunan University（湖南大学）；Peng Cheng Laboratory（鹏城实验室）；Changsha University of Science and Technology（长沙理工大学）
