Tackling Modern Challenges in Statistics: Integrating Privacy, Distributed Learning, and Data Heterogeneity Abhinav Chakraborty

Format:

Book

Thesis/Dissertation

Author/Creator:

Chakraborty, Abhinav, author.

Contributor:

University of Pennsylvania. Statistics and Data Science., degree granting institution.

Language:

English

Subjects (All):

Statistics.

Applied mathematics.

Information science.

0463.

0723.

0364.

Local Subjects:

Statistics.

Applied mathematics.

Information science.

0463.

0723.

0364.

Physical Description:

1 electronic resource (337 pages)

Contained In:

Dissertations Abstracts International 86-12A

Place of Publication:

Ann Arbor : ProQuest Dissertations and Theses, 2025

Language Note:

English

Summary:

In modern statistical applications, data are increasingly distributed across multiple sources, such as hospitals, mobile devices, and research institutions, and often contain sensitive information subject to privacy constraints. This decentralized and privacy-sensitive landscape poses fundamental challenges for statistical learning. In particular, classical methods based on centralized data aggregation are infeasible or undesirable, necessitating the development of distributed inference methods that rigorously preserve privacy while maintaining statistical efficiency.This thesis investigates the theoretical foundations of statistical inference under privacy and communication constraints in federated environments. We focus on the framework of Federated Differential Privacy (FDP), which extends classical differential privacy to settings where multiple servers apply local privacy mechanisms to their data before communicating with a central aggregator. Our work develops sharp information-theoretic bounds, rate-optimal procedures, and new techniques that characterize the fundamental trade-offs between privacy, accuracy, and heterogeneity.The thesis consists of four main contributions:We study nonparametric regression under FDP constraints, deriving minimax optimal rates for both global and pointwise estimation over Besov classes. Our results unify and extend existing theory for central and local differential privacy.We analyze nonparametric goodness-of-fit testing in the federated setting, establishing mini-max separation rates and constructing adaptive testing procedures. The analysis reveals new privacy-induced phase transitions absent in estimation problems.We investigate federated transfer learning under posterior drift for binary classification. We derive minimax rates for excess risk, accounting for heterogeneous privacy budgets and data quality across servers, and develop adaptive classifiers that remain optimal across regimes.We establish optimal rates for functional mean estimation under privacy constraints in federated systems. Our analysis covers both common and independent design settings and develops new lower-bound techniques that handle server heterogeneity.Together, these results provide a unified framework for understanding the statistical limits of distributed inference under privacy constraints. They advance the theory of privacy-preserving learning in federated environments and offer methodological tools with practical relevance for applications in healthcare, finance, and beyond

Notes:

Source: Dissertations Abstracts International, Volume: 86-12, Section: A.

Advisors: Cai, T. Tony Committee members: Katsevich, Eugene; Roth, Aaron; Su, Weijie

Ph.D. University of Pennsylvania 2025

Local Notes:

School code: 0175

ISBN:

9798280757912

Access Restriction:

Restricted for use by site license