Semisupervised regression in latent structure networks on unknown manifolds

IF 1.3 Q3 COMPUTER SCIENCE, THEORY & METHODS Applied Network Science Pub Date : 2023-11-07 DOI:10.1007/s41109-023-00598-9
Aranyak Acharyya, Joshua Agterberg, Michael W. Trosset, Youngser Park, Carey E. Priebe
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Abstract

Abstract Random graphs are increasingly becoming objects of interest for modeling networks in a wide range of applications. Latent position random graph models posit that each node is associated with a latent position vector, and that these vectors follow some geometric structure in the latent space. In this paper, we consider random dot product graphs, in which an edge is formed between two nodes with probability given by the inner product of their respective latent positions. We assume that the latent position vectors lie on an unknown one-dimensional curve and are coupled with a response covariate via a regression model. Using the geometry of the underlying latent position vectors, we propose a manifold learning and graph embedding technique to predict the response variable on out-of-sample nodes, and we establish convergence guarantees for these responses. Our theoretical results are supported by simulations and an application to Drosophila brain data.
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未知流形上潜在结构网络的半监督回归
在广泛的应用中,随机图越来越成为网络建模的兴趣对象。潜在位置随机图模型假设每个节点都与潜在位置向量相关联,并且这些向量在潜在空间中遵循某些几何结构。在本文中,我们考虑随机点积图,其中两个节点之间形成一条边,其概率由其各自潜在位置的内积给出。我们假设潜在位置向量位于未知的一维曲线上,并通过回归模型与响应协变量耦合。利用潜在位置向量的几何结构,我们提出了一种流形学习和图嵌入技术来预测样本外节点上的响应变量,并建立了这些响应的收敛保证。我们的理论结果得到了模拟和果蝇大脑数据应用的支持。
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来源期刊
Applied Network Science
Applied Network Science Multidisciplinary-Multidisciplinary
CiteScore
4.60
自引率
4.50%
发文量
74
审稿时长
5 weeks
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