多尺度高斯图模型推断
Inference of Multiscale Gaussian Graphical Model
AI总结：
本文提出多尺度图Lasso方法，通过同时进行聚类与图推断提升网络可解释性，应用于基因组和微生物数据。
摘要：
高斯图模型（GGMs）广泛用于高维数据分析以合成变量间相互作用。本文探讨了一种不同范式，其中聚类不是知识驱动而是与图推断同时进行。我们引入了多尺度图Lasso（MGLasso）方法，通过凸聚类方法（k-means松弛和层次聚类）估计聚类，并通过邻域选择方案同时推断条件独立图。MGLasso扩展并推广了稀疏组融合Lasso问题到无向图模型。我们使用连续性与Nesterov平滑的收缩阈值算法（CONESTA）提出正则化路径，同时保持Lasso惩罚不变。在合成数据上的实验比较了模型与现有聚类和网络推断方法的性能，并应用于肠道微生物组数据和松树甲基化混合转录组数据。
英文摘要：
Gaussian Graphical Models (GGMs) are widely used in high-dimensional data analysis to synthesize the interaction between variables. In many applications, such as genomics or image analysis, graphical models rely on sparsity and clustering to reduce dimensionality and improve performances. This paper explores a slightly different paradigm where clustering is not knowledge-driven but performed simultaneously with the graph inference task. We introduce a novel Multiscale Graphical Lasso (MGLasso) to improve networks interpretability by proposing graphs at different granularity levels. The method estimates clusters through a convex clustering approach - a relaxation of k-means, and hierarchical clustering. The conditional independence graph is simultaneously inferred through a neighborhood selection scheme for undirected graphical models. MGLasso extends and generalizes the sparse group fused lasso problem to undirected graphical models. We use continuation with Nesterov smoothing in a shrinkage-thresholding algorithm (CONESTA) to propose a regularization path of solutions along the group fused Lasso penalty, while the Lasso penalty is kept constant. Extensive experiments on synthetic data compare the performances of our model to state-of-the-art clustering methods and network inference models. Applications to gut microbiome data and poplar's methylation mixed with transcriptomic data are presented.
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