MIT Libraries homeMIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Bounds on inference

Author(s)
Medard, Muriel; Christiansen, Mark M.; Duffy, Ken R.; Tessaro, Stefano; Calmon, Flavio du Pin; Varia, Mayank H.; ... Show more Show less
Thumbnail
DownloadMedard_Bounds on.pdf (219.2Kb)
OPEN_ACCESS_POLICY

Open Access Policy

Creative Commons Attribution-Noncommercial-Share Alike

Terms of use
Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
Metadata
Show full item record
Abstract
Lower bounds for the average probability of error of estimating a hidden variable X given an observation of a correlated random variable Y, and Fano's inequality in particular, play a central role in information theory. In this paper, we present a lower bound for the average estimation error based on the marginal distribution of X and the principal inertias of the joint distribution matrix of X and Y. Furthermore, we discuss an information measure based on the sum of the largest principal inertias, called k-correlation, which generalizes maximal correlation. We show that k-correlation satisfies the Data Processing Inequality and is convex in the conditional distribution of Y given X. Finally, we investigate how to answer a fundamental question in inference and privacy: given an observation Y, can we estimate a function f(X) of the hidden random variable X with an average error below a certain threshold? We provide a general method for answering this question using an approach based on rate-distortion theory.
Date issued
2013-10
URI
http://hdl.handle.net/1721.1/90435
Department
Lincoln Laboratory; Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Research Laboratory of Electronics
Journal
Proceedings of the 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Calmon, Flavio P., Mayank Varia, Muriel Medard, Mark M. Christiansen, Ken R. Duffy, and Stefano Tessaro. “Bounds on Inference.” 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton) (October 2013).
Version: Author's final manuscript
ISBN
978-1-4799-3410-2
978-1-4799-3409-6

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries homeMIT Libraries logo

Find us on

Twitter Facebook Instagram YouTube RSS

MIT Libraries navigation

SearchHours & locationsBorrow & requestResearch supportAbout us
PrivacyPermissionsAccessibility
MIT
Massachusetts Institute of Technology
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.