國立虎尾科技大學 |

Data Permutation Recovery From Noisy Data : = Error Probability and Privacy.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Data Permutation Recovery From Noisy Data :/
其他題名:	Error Probability and Privacy.
作者:	Jeong, Minoh.
面頁冊數:	1 online resource (180 pages)
附註:	Source: Dissertations Abstracts International, Volume: 85-12, Section: A.
Contained By:	Dissertations Abstracts International85-12A.
標題:	Statistics. -
電子資源:	click for full text (PQDT)
ISBN:	9798383162996

Data Permutation Recovery From Noisy Data : = Error Probability and Privacy.
Jeong, Minoh.

Data Permutation Recovery From Noisy Data :Error Probability and Privacy. - 1 online resource (180 pages)

Source: Dissertations Abstracts International, Volume: 85-12, Section: A.

Thesis (Ph.D.)--University of Minnesota, 2024.

Includes bibliographical references

This doctoral thesis investigates the data permutation recovery problem from noisy observations, a fundamental challenge at the intersection of data science and privacy-preserving technologies. The main question is: Given a noisy observation of data, according to which permutation was the original data sorted? This thesis addresses both the exact and approximate permutation recovery problems under various noise conditions. It begins by formulating the permutation recovery problem within the statistical hypothesis testing framework, and characterizes the linear regime, where the true permutation can be optimally estimated by only a linear transformation of the observation and a sorting operation. In particular, under Gaussian data and noise, this thesis derives the necessary and sufficient conditions for the linear regime in terms of the noise covariance matrix. Subsequently, this thesis shifts the focus to the examination of the error probability associated with linear decoders in the presence of Gaussian noise, but arbitrary data distribution. This analysis reveals the noise-dominated nature of the permutation recovery problem, illustrating how the error probability scales in both low- and high-noise regimes, and providing insights into the behavior of the error probability under different noise and data distributions. Specifically, the error probability of the permutation recovery problem grows linearly in the noise standard deviation σ in the low-noise regime, implying the noise-dominated nature of the problem. Advancing into the realm of data privacy, the thesis explores the private ranking recovery problem, aiming to establish fundamental trade-offs between estimation accuracy and privacy. Leveraging differential privacy metrics, it evaluates the effectiveness of various privacy-preserving mechanisms while ensuring the fidelity of the ranking recovery. Regarding the generalized permutation recovery problem, this thesis also proposes an approximate version of it. It demonstrates that this approximate version leads to an error probability having sub-linear behavior in σ in the low-noise regime, which is a notable difference with respect to the exact recovery. This finding highlights the potential of approximate recovery in enhancing the robustness and efficiency of permutation recovery. In summary, the thesis contributes significantly to our understanding of permutation recovery in noisy and privacy-sensitive environments. The thesis not only advances theoretical foundations but also provides practical strategies for tackling the challenges inherent in recovering data permutations, thereby offering valuable perspectives for advancements in data processing and privacy-preserving techniques.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798383162996Subjects--Topical Terms:

556824
Statistics.
Subjects--Index Terms:

AsymptoticIndex Terms--Genre/Form:

554714
Electronic books.

Data Permutation Recovery From Noisy Data : = Error Probability and Privacy.
LDR:04164ntm a22004217 4500 001 1150208
005 20241022111615.5
006 m o d
007 cr bn ---uuuuu
008 250605s2024 xx obm 000 0 eng d
020 $a 9798383162996
035 $a (MiAaPQ)AAI31300068
035 $a AAI31300068
040 $a MiAaPQ $b eng $c MiAaPQ $d NTU
100 1 $a Jeong, Minoh. $3 1476648
245 1 0 $a Data Permutation Recovery From Noisy Data : $b Error Probability and Privacy.
264 0 $c 2024
300 $a 1 online resource (180 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: 85-12, Section: A.
500 $a Advisor: Cardone, Martina.
502 $a Thesis (Ph.D.)--University of Minnesota, 2024.
504 $a Includes bibliographical references
520 $a This doctoral thesis investigates the data permutation recovery problem from noisy observations, a fundamental challenge at the intersection of data science and privacy-preserving technologies. The main question is: Given a noisy observation of data, according to which permutation was the original data sorted? This thesis addresses both the exact and approximate permutation recovery problems under various noise conditions. It begins by formulating the permutation recovery problem within the statistical hypothesis testing framework, and characterizes the linear regime, where the true permutation can be optimally estimated by only a linear transformation of the observation and a sorting operation. In particular, under Gaussian data and noise, this thesis derives the necessary and sufficient conditions for the linear regime in terms of the noise covariance matrix. Subsequently, this thesis shifts the focus to the examination of the error probability associated with linear decoders in the presence of Gaussian noise, but arbitrary data distribution. This analysis reveals the noise-dominated nature of the permutation recovery problem, illustrating how the error probability scales in both low- and high-noise regimes, and providing insights into the behavior of the error probability under different noise and data distributions. Specifically, the error probability of the permutation recovery problem grows linearly in the noise standard deviation σ in the low-noise regime, implying the noise-dominated nature of the problem. Advancing into the realm of data privacy, the thesis explores the private ranking recovery problem, aiming to establish fundamental trade-offs between estimation accuracy and privacy. Leveraging differential privacy metrics, it evaluates the effectiveness of various privacy-preserving mechanisms while ensuring the fidelity of the ranking recovery. Regarding the generalized permutation recovery problem, this thesis also proposes an approximate version of it. It demonstrates that this approximate version leads to an error probability having sub-linear behavior in σ in the low-noise regime, which is a notable difference with respect to the exact recovery. This finding highlights the potential of approximate recovery in enhancing the robustness and efficiency of permutation recovery. In summary, the thesis contributes significantly to our understanding of permutation recovery in noisy and privacy-sensitive environments. The thesis not only advances theoretical foundations but also provides practical strategies for tackling the challenges inherent in recovering data permutations, thereby offering valuable perspectives for advancements in data processing and privacy-preserving techniques.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Statistics. $3 556824
650 4 $a Computer science. $3 573171
650 4 $a Information science. $3 561178
653 $a Asymptotic
653 $a Linear regime
653 $a Data permutation recovery
653 $a Privacy
653 $a Ranking recovery
653 $a Recovery problem
655 7 $a Electronic books. $2 local $3 554714
690 $a 0463
690 $a 0984
690 $a 0800
690 $a 0723
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Minnesota. $b Electrical/Computer Engineering. $3 1182326
773 0 $t Dissertations Abstracts International $g 85-12A.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31300068 $z click for full text (PQDT)