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Optimization and Statistical Inferen...

Niu, Xiaochun,

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Optimization and Statistical Inference in Networks /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Optimization and Statistical Inference in Networks // Xiaochun Niu.
Author:	Niu, Xiaochun,
Description:	1 electronic resource (268 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-02, Section: B.
Contained By:	Dissertations Abstracts International86-02B.
Subject:	Statistics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31489624
ISBN:	9798384016557

Optimization and Statistical Inference in Networks /
Niu, Xiaochun,

Optimization and Statistical Inference in Networks /Xiaochun Niu. - 1 electronic resource (268 pages)

Source: Dissertations Abstracts International, Volume: 86-02, Section: B.

This dissertation studies optimization and statistical inference within large networks, focusing on distributed optimization and community detection problems. We aim to improve algorithm efficiency and deepen our understanding of complex networks.Distributed optimization problems aim to collaboratively optimize objectives across multi-agent systems, where significant challenges arise due to system heterogeneity. Existing distributed methods often overlook the heterogeneity in agents' computational capabilities, limiting their effectiveness. To address this, Chapters 2 and 3 introduce distributed hybrid methods that utilize these heterogeneous capabilities. We begin with a federated network, proposing a hybrid method that allows agents to perform updates based on their computational capabilities, either gradient-type or Newton-type. This method enables agents with powerful hardware to perform local Newton-type updates, thereby accelerating the overall system performance. In addition, we extend these hybrid methods to general graph topologies, tackling distributed consensus and network flow problems through different distributed approximations of Newton's methods. We prove the linear convergence rates of these methods. Numerical studies indicate that increasing the number of agents performing Newton-type updates can accelerate the overall convergence, demonstrating the method's efficacy.Community recovery is the problem of identifying latent community structures within large networks using observed data. Chapters 4 and 5 focus on exact community recovery in a family of probabilistic graph models with geometric embeddings, within the logarithmic-degree regime. These models reflect the edge-transitive properties typical of real-world networks. Our study begins with the Geometric Stochastic Block Model (GSBM), where vertices have unknown community labels and known locations in ℝd , generated by a Poisson point process. Edges are formed based on the community labels, but only between vertices within a certain distance. We identify the information-theoretic threshold for exact recovery and prove its achievability through a linear-time, two-phase algorithm: the first phase produces an almost-exact labeling via a local propagation scheme, and the second phase refines the labels. In addition, we propose the Geometric Hidden Community Model (GHCM) as an extension, including geometric versions of ℤ2- synchronization and submatrix localization as special cases. Under a mild distinctness in distributions assumption, we identify the information-theoretic threshold for this general model via a Chernoff-Hellinger divergence criterion.

English

ISBN: 9798384016557Subjects--Topical Terms:

517247
Statistics.
Subjects--Index Terms:

Chernoff-Hellinger divergence criterion

Optimization and Statistical Inference in Networks /
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520 $a This dissertation studies optimization and statistical inference within large networks, focusing on distributed optimization and community detection problems. We aim to improve algorithm efficiency and deepen our understanding of complex networks.Distributed optimization problems aim to collaboratively optimize objectives across multi-agent systems, where significant challenges arise due to system heterogeneity. Existing distributed methods often overlook the heterogeneity in agents' computational capabilities, limiting their effectiveness. To address this, Chapters 2 and 3 introduce distributed hybrid methods that utilize these heterogeneous capabilities. We begin with a federated network, proposing a hybrid method that allows agents to perform updates based on their computational capabilities, either gradient-type or Newton-type. This method enables agents with powerful hardware to perform local Newton-type updates, thereby accelerating the overall system performance. In addition, we extend these hybrid methods to general graph topologies, tackling distributed consensus and network flow problems through different distributed approximations of Newton's methods. We prove the linear convergence rates of these methods. Numerical studies indicate that increasing the number of agents performing Newton-type updates can accelerate the overall convergence, demonstrating the method's efficacy.Community recovery is the problem of identifying latent community structures within large networks using observed data. Chapters 4 and 5 focus on exact community recovery in a family of probabilistic graph models with geometric embeddings, within the logarithmic-degree regime. These models reflect the edge-transitive properties typical of real-world networks. Our study begins with the Geometric Stochastic Block Model (GSBM), where vertices have unknown community labels and known locations in ℝd , generated by a Poisson point process. Edges are formed based on the community labels, but only between vertices within a certain distance. We identify the information-theoretic threshold for exact recovery and prove its achievability through a linear-time, two-phase algorithm: the first phase produces an almost-exact labeling via a local propagation scheme, and the second phase refines the labels. In addition, we propose the Geometric Hidden Community Model (GHCM) as an extension, including geometric versions of ℤ2- synchronization and submatrix localization as special cases. Under a mild distinctness in distributions assumption, we identify the information-theoretic threshold for this general model via a Chernoff-Hellinger divergence criterion.
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653 $a Geometric Stochastic Block Model
653 $a System heterogeneity
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