Inference for Multiple Heterogeneous Networks with a Common Invariant Subspace.

IF 4.3 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Journal of Machine Learning Research Pub Date : 2021-03-01
Jesús Arroyo, Avanti Athreya, Joshua Cape, Guodong Chen, Carey E Priebe, Joshua T Vogelstein
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引用次数: 0

Abstract

The development of models and methodology for the analysis of data from multiple heterogeneous networks is of importance both in statistical network theory and across a wide spectrum of application domains. Although single-graph analysis is well-studied, multiple graph inference is largely unexplored, in part because of the challenges inherent in appropriately modeling graph differences and yet retaining sufficient model simplicity to render estimation feasible. This paper addresses exactly this gap, by introducing a new model, the common subspace independent-edge multiple random graph model, which describes a heterogeneous collection of networks with a shared latent structure on the vertices but potentially different connectivity patterns for each graph. The model encompasses many popular network representations, including the stochastic blockmodel. The model is both flexible enough to meaningfully account for important graph differences, and tractable enough to allow for accurate inference in multiple networks. In particular, a joint spectral embedding of adjacency matrices-the multiple adjacency spectral embedding-leads to simultaneous consistent estimation of underlying parameters for each graph. Under mild additional assumptions, the estimates satisfy asymptotic normality and yield improvements for graph eigenvalue estimation. In both simulated and real data, the model and the embedding can be deployed for a number of subsequent network inference tasks, including dimensionality reduction, classification, hypothesis testing, and community detection. Specifically, when the embedding is applied to a data set of connectomes constructed through diffusion magnetic resonance imaging, the result is an accurate classification of brain scans by human subject and a meaningful determination of heterogeneity across scans of different individuals.

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具有共同不变子空间的多个异构网络的推理。
开发用于分析来自多个异构网络的数据的模型和方法在统计网络理论和广泛的应用领域中都具有重要意义。虽然单图分析已被广泛研究,但多图推断在很大程度上还未被探索,部分原因是在对图差异进行适当建模的同时又要保持足够的模型简洁性以保证估算的可行性所面临的固有挑战。本文正是为了弥补这一不足,引入了一个新模型--公共子空间独立边多随机图模型,该模型描述了具有共享顶点潜在结构但每个图的连接模式可能不同的异构网络集合。该模型涵盖了许多流行的网络表示法,包括随机块模型。该模型既具有足够的灵活性,可以有意义地解释重要的图差异,又具有足够的可操作性,可以在多个网络中进行精确推断。特别是,邻接矩阵的联合谱嵌入--多邻接谱嵌入--可同时一致地估计每个图的基本参数。在温和的附加假设条件下,估计值满足渐近正态性,并改进了图特征值估计。在模拟数据和真实数据中,该模型和嵌入可用于一系列后续网络推断任务,包括降维、分类、假设检验和群落检测。具体来说,当嵌入应用于通过扩散磁共振成像构建的连接组数据集时,结果是按人类主体对大脑扫描进行了准确分类,并对不同个体扫描的异质性做出了有意义的判断。
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来源期刊
Journal of Machine Learning Research
Journal of Machine Learning Research 工程技术-计算机:人工智能
CiteScore
18.80
自引率
0.00%
发文量
2
审稿时长
3 months
期刊介绍: The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online. JMLR has a commitment to rigorous yet rapid reviewing. JMLR seeks previously unpublished papers on machine learning that contain: new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature; experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems; accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods; formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks; development of new analytical frameworks that advance theoretical studies of practical learning methods; computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.
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