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Activity Number:
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334
- Network Data and Models
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Type:
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Contributed
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Date/Time:
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Tuesday, August 9, 2022 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistical Learning and Data Science
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Abstract #321016
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Title:
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Central Limit Theorems and Hypothesis Testing for Multiple Networks with Common Invariant Subspaces
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Author(s):
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Runbing Zheng* and Minh Tang
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Companies:
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North Carolina State University and North Carolina State University
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Keywords:
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multiple heterogeneous graphs;
distributed PCA;
central limit theorems;
hypothesis testing
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Abstract:
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We study the problem of estimating the left and right singular vectors for heterogeneous random graphs with a common structure. We analyze an algorithm that ?rst estimates the orthogonal projection matrices corresponding to the left and right subspaces for each individual graph then computes the average of these projection matrices and ?nally ?nds the matrices whose columns are the eigenvectors corresponding to the d largest eigenvalues of these sample averages. We show that the estimate of the left and right singular vectors has row-wise ?uctuationsare normally distributed around the rows of the true singular vectors. We then consider a two-sample hypothesis test for the null hypothesis that two graphs have the same probabilities matrices. We present a test statistic whose limiting distribution converges to a central ?2 (resp. non-central ?2) under the null (resp. alternative) hypothesis. Finally, we discuss how the estimation procedure, which is developed for graph setting, can also be used for distributed PCA; in particular we derive normal approximations for the rows of the estimated eigenvectors using distributed PCA when the data exhibit a spiked covariance matrix structure.
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Authors who are presenting talks have a * after their name.
