Exploration of Kacs walk and analysis of bayesian distributed computing
Abstract
This is approved for public releaseThis project has two themes: (i) Analysis of Kacs random walk and developing its applications and (ii) Developing Bayesian methodology for distributed systems.The first part of my proposed research will develop new tools in probability theory with the primary goal of answering foundational questions in mathematical physics and computational statistics that have a similar mathematical structure. The second part of the proposed research focuses on the theoretical properties of estimation in distributedsettings, an area of study whose importance has increased drastically in light of the emergence of big data and large distributed networks. The ability to collect massive data sets has moved modern data analysis into the cloud, where massive data sets are split across huge networks of computers. As more and more analysis moves intodistributed settings, it is important to be able to evaluate procedures that perform estimation when there arelimits on communication across the network. Limiting the amount of communication is of great practical importance because transmission of data across a network is relatively slow and can impose costs on other users. Data transmission is a clear bottleneck as data sizes increase, so operating under communication constraints isnecessary to ensure practical run times for very large data. In more technical terms, the statistical goal of the proposed research is to determine the minimax rates for distributed estimators under communication constraints. The minimax rate describes the rate of convergence for the best worst-case performance and is a very general method of evaluating the difficulty of an estimation problem. In the absence of communication constraints, the problem reduces to the usual rate calculation (as we can transmit all of the data to one machine and use the usual estimator), so the communication constraints are truly central to our work.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 05, 2021
- Source ID
- N000142112664
Entities
People
- Natesh Pillai
Organizations
- Office of Naval Research
- President and Fellows of Harvard College
- United States Navy