東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Linked to FindBook

Google Book

Amazon

博客來

Testing in Network Models with Community Structure.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Testing in Network Models with Community Structure./
Author:	Zhang, Linfan.
Description:	1 online resource (171 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-03, Section: B.
Contained By:	Dissertations Abstracts International84-03B.
Subject:	Statistics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29392303click for full text (PQDT)
ISBN:	9798845720368

Testing in Network Models with Community Structure.
Zhang, Linfan.

Testing in Network Models with Community Structure. - 1 online resource (171 pages)

Source: Dissertations Abstracts International, Volume: 84-03, Section: B.

Thesis (Ph.D.)--University of California, Los Angeles, 2022.

Includes bibliographical references

We consider the problem of testing in network models with community structures. In the first part, we propose a goodness-of-fit test for degree-corrected stochastic block models (DCSBM). The test is based on an adjusted chi-square statistic for measuring equality of means among groups of n multinomial distributions with d1,...,dn observations. In the context of network models, the number of multinomials, n, grows much faster than the number of observations, di, corresponding to the degree of node i, hence the setting deviates from classical asymptotics. We show that a simple adjustment allows the statistic to converge in distribution, under null, as long as the harmonic mean of i grows to infinity. When applied sequentially, the test can also be used to determine the number of communities. Since the test statistic does not rely on a specific alternative, its utility goes beyond sequential testing and can be used to simultaneously test against a wide range of alternatives outside the DCSBM family. We show the effectiveness of the approach by extensive numerical experiments with simulated and real data. In the second part, we provide theoretical guarantees for label consistency in generalized k-means problems, with an emphasis on the overfitted case where the number of clusters used by the algorithm is more than the ground truth. We provide conditions under which the estimated labels are close to a refinement of the true cluster labels. We consider both exact and approximate recovery of the labels. Our results hold for any constant-factor approximation to the k-means problem. The results are also model-free and only based on bounds on the maximum or average distance of the data points to the true cluster centers. These centers themselves are loosely defined and can be taken to be any set of points for which the aforementioned distances can be controlled. We show the usefulness of the results with applications to some manifold clustering problems.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798845720368Subjects--Topical Terms:

517247
Statistics.
Subjects--Index Terms:

ClusteringIndex Terms--Genre/Form:

542853
Electronic books.

Testing in Network Models with Community Structure.
LDR:03392nmm a2200421K 4500 001 2356263
005 20230612072251.5
006 m o d
007 cr mn ---uuuuu
008 241011s2022 xx obm 000 0 eng d
020 $a 9798845720368
035 $a (MiAaPQ)AAI29392303
035 $a AAI29392303
040 $a MiAaPQ $b eng $c MiAaPQ $d NTU
100 1 $a Zhang, Linfan. $3 3696743
245 1 0 $a Testing in Network Models with Community Structure.
264 0 $c 2022
300 $a 1 online resource (171 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 84-03, Section: B.
500 $a Advisor: Amini, Arash Ali.
502 $a Thesis (Ph.D.)--University of California, Los Angeles, 2022.
504 $a Includes bibliographical references
520 $a We consider the problem of testing in network models with community structures. In the first part, we propose a goodness-of-fit test for degree-corrected stochastic block models (DCSBM). The test is based on an adjusted chi-square statistic for measuring equality of means among groups of n multinomial distributions with d1,...,dn observations. In the context of network models, the number of multinomials, n, grows much faster than the number of observations, di, corresponding to the degree of node i, hence the setting deviates from classical asymptotics. We show that a simple adjustment allows the statistic to converge in distribution, under null, as long as the harmonic mean of i grows to infinity. When applied sequentially, the test can also be used to determine the number of communities. Since the test statistic does not rely on a specific alternative, its utility goes beyond sequential testing and can be used to simultaneously test against a wide range of alternatives outside the DCSBM family. We show the effectiveness of the approach by extensive numerical experiments with simulated and real data. In the second part, we provide theoretical guarantees for label consistency in generalized k-means problems, with an emphasis on the overfitted case where the number of clusters used by the algorithm is more than the ground truth. We provide conditions under which the estimated labels are close to a refinement of the true cluster labels. We consider both exact and approximate recovery of the labels. Our results hold for any constant-factor approximation to the k-means problem. The results are also model-free and only based on bounds on the maximum or average distance of the data points to the true cluster centers. These centers themselves are loosely defined and can be taken to be any set of points for which the aforementioned distances can be controlled. We show the usefulness of the results with applications to some manifold clustering problems.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Statistics. $3 517247
650 4 $a Statistical physics. $3 536281
650 4 $a Applied mathematics. $3 2122814
650 4 $a Systems science. $3 3168411
653 $a Clustering
653 $a Degree-corrected stochastic block models
653 $a Goodness-of-fit
653 $a k-means
653 $a Network
653 $a Overfitting
655 7 $a Electronic books. $2 lcsh $3 542853
690 $a 0463
690 $a 0217
690 $a 0364
690 $a 0790
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a University of California, Los Angeles. $b Statistics 0891. $3 2095317
773 0 $t Dissertations Abstracts International $g 84-03B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29392303 $z click for full text (PQDT)