A computational approach to maximum likelihood thresholds for colored Gaussian graphical models
本文通过几何方法和拓扑数据分析解决彩色高斯图模型的最大似然阈值计算问题,减少样本需求并克服传统方法的瓶颈。
本文通过几何方法和拓扑数据分析解决彩色高斯图模型的最大似然阈值计算问题,减少样本需求并克服传统方法的瓶颈。
该研究解决了多色点集的欧几里得最小生成树问题,通过引入月牙状结构,并证明了随机情况下其期望成本收敛于与点数平方根成比例的常数。
为解决生物测定活性预测数据有限的问题,本文提出Monroe模型,通过扩大预训练规模、改进图表示等方法提高分子基础模型性能。
Persistent diagrams lack a natural vector space structure, and existing statistical methods struggle to integrate effectively with downstream predictive tasks. This work addresses these limitations by treating persistent diagrams as survival data and introduces a unified framework based on persistence survival functions. For the first time, this approach simultaneously enables hypothesis testing, effect size quantification, and 1-Wasserstein stable vectorization from a single interpretable representation. By integrating survival analysis with nonparametric two-sample testing, the method demonstrates well-calibrated type I error control and high statistical power on synthetic manifolds. It achieves strong performance across 14 benchmark tasks involving graphs and 3D point clouds and is successfully applied to fMRI-based brain functional connectivity analysis.
This work addresses the scalability bottleneck in subgraph pattern detection within large-scale graphs, a challenge rooted in the NP-completeness of the problem, by introducing the DETR paradigm to this task for the first time. The proposed method formulates subgraph detection as a set prediction problem, leveraging a graph neural network to encode the target graph, learnable query embeddings, and a Transformer decoder to jointly predict all pattern instances in an end-to-end manner via bipartite matching loss. This framework supports both exact and approximate pattern matching, thereby overcoming the limitation of traditional approaches that are restricted to exact structural matches. Experiments demonstrate that the method efficiently detects diverse patterns of up to 50 nodes in graphs containing 1,000 nodes, achieving an AP₁₀₀ of 91.2 on functional group detection in the ChEMBL molecular dataset.
本文通过几何方法和拓扑数据分析解决彩色高斯图模型的最大似然阈值计算问题,减少样本需求并克服传统方法的瓶颈。
该研究解决了多色点集的欧几里得最小生成树问题,通过引入月牙状结构,并证明了随机情况下其期望成本收敛于与点数平方根成比例的常数。
为解决生物测定活性预测数据有限的问题,本文提出Monroe模型,通过扩大预训练规模、改进图表示等方法提高分子基础模型性能。
Persistent diagrams lack a natural vector space structure, and existing statistical methods struggle to integrate effectively with downstream predictive tasks. This work addresses these limitations by treating persistent diagrams as survival data and introduces a unified framework based on persistence survival functions. For the first time, this approach simultaneously enables hypothesis testing, effect size quantification, and 1-Wasserstein stable vectorization from a single interpretable representation. By integrating survival analysis with nonparametric two-sample testing, the method demonstrates well-calibrated type I error control and high statistical power on synthetic manifolds. It achieves strong performance across 14 benchmark tasks involving graphs and 3D point clouds and is successfully applied to fMRI-based brain functional connectivity analysis.
This work addresses the scalability bottleneck in subgraph pattern detection within large-scale graphs, a challenge rooted in the NP-completeness of the problem, by introducing the DETR paradigm to this task for the first time. The proposed method formulates subgraph detection as a set prediction problem, leveraging a graph neural network to encode the target graph, learnable query embeddings, and a Transformer decoder to jointly predict all pattern instances in an end-to-end manner via bipartite matching loss. This framework supports both exact and approximate pattern matching, thereby overcoming the limitation of traditional approaches that are restricted to exact structural matches. Experiments demonstrate that the method efficiently detects diverse patterns of up to 50 nodes in graphs containing 1,000 nodes, achieving an AP₁₀₀ of 91.2 on functional group detection in the ChEMBL molecular dataset.