论文检索

低秩张量的统计推断：异方差、次高斯性与应用AI 解读

In this paper, we consider inference and uncertainty quantification for low Tucker rank tensors with additive noise in the high-dimensional regime. Focusing on the output of the higher-order orthogonal iteration (HOOI) algorithm, a commonly used algorithm for tensor singular value decomposition, we establish nonasymptotic distributional theory and study how to construct confidence regions and intervals for both the estimated singular vectors and the tensor entries in the…

多层度修正随机块模型中的联合谱聚类AI 解读

Modern network datasets are often composed of multiple layers, resulting in collections of networks over the same set of vertices but with potentially different connectivity patterns on each network. These data require models and methods that are flexible enough to capture local and global differences across the networks while at the same time being parsimonious and tractable to yield computationally efficient and theoretically sound solutions that are capable of aggregating…

利用逐行张量扰动界估计高阶混合社群成员关系AI 解读

Higher-order multiway data is ubiquitous in machine learning and statistics and often exhibits community-like structures, where each component (node) along each different mode has a community membership associated with it. In this article we propose the sub-Gaussian) tensor mixed-membership blockmodel, a generalization of the tensor blockmodel positing that memberships need not be discrete, but instead are convex combinations of latent communities. We establish the…