Limit results for distributed estimation of invariant subspaces in multiple networks inference and PCA

[2206.04306] Limit results for distributed estimation of invariant subspaces in multiple networks inference and PCA Skip to main content Search Submit Donate Log in Mathematics > Statistics Theory arXiv:2206.04306 (math) [Submitted on 9 Jun 2022 ( v1 ), last revised 27 Aug 2026 (this version, v6)] Title: Limit results for distributed estimation of invariant subspaces in multiple networks inference and PCA Authors: Runbing Zheng , Minh Tang View PDF HTML (experimental) Abstract: Several statistical problems, such as multiple heterogeneous graph analysis, distributed PCA, integrative data analysis, and simultaneous dimension reduction of images, can involve a collection of $m$ matrices whose leading subspaces $U^{(i)}$ consist of a shared subspace $U_c$ and individual subspaces $U_s^{(i)}$. We consider a distributed estimation procedure that first obtains $\hat U^{(i)}$ as the leading singular vectors for each observed noisy matrix, then computes the leading left singular vectors of the concatenated matrix $[\hat U^{(1)}|\hat U^{(2)}|\dots|\hat U^{(m)}]$ as $\hat U_c$, and finally computes the leading singular vectors of the projection of each $\hat U^{(i)}$ onto the orthogonal complement of $\hat U_c$ as $\hat U_s^{(i)}$. In this paper, we provide a framework for deriving limit results for such distributed estimation procedures, including expansions of estimation errors in both common and individual subspaces and their asymptotically normal approximations. We apply this framework specifically to (1) parameter estimation for multiple heterogeneous random graphs with shared subspaces, and (2) distributed PCA for independent sub-Gaussian random vectors with spiked covariance structures. Leveraging these results, we also consider a two-sample test for the null hypothesis that a pair of random graphs have the same edge probabilities, and present a test statistic whose limiting distribution converges to a central (resp., non-central) $\chi^2$ distribution under the null (resp., local alternative) hypothesis. Subjects: Statistics Theory (math.ST) Cite as: arXiv:2206.04306 [math.ST] (or arXiv:2206.04306v6 [math.ST] for this version) https://doi.org/10.48550/arXiv.2206.04306 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Runbing Zheng [ view email ] [v1] Thu, 9 Jun 2022 06:54:00 UTC (6,453 KB) [v2] Mon, 1 Aug 2022 20:14:48 UTC (5,718 KB) [v3] Tue, 21 Nov 2023 05:50:02 UTC (5,806 KB) [v4] Wed, 22 May 2024 06:40:09 UTC (5,812 KB) [v5] Mon, 8 Dec 2025 20:35:06 UTC (5,740 KB) [v6] Thu, 27 Aug 2026 21:30:40 UTC (5,749 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.ST < prev | next > new | recent | 2022-06 Change to browse by: math stat stat.TH References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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