Calmon, Flavio P. and Varia, Mayank and Medard, Muriel and Christiansen, Mark M. and Duffy, Ken R. and Tessaro, Stefano
(2013)
Bounds on inference.
Working Paper.
arXiv.org.
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 kcorrelation, which generalizes
maximal correlation. We show that kcorrelation 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 ratedistortion theory.
Item Type: 
Monograph
(Working Paper)

Additional Information: 
Paper given at the 51st Allerton Conference on Communication, Control, and Computing (2013). This work is sponsored by the Intelligence Advanced Research Projects
Activity under Air Force Contract FA872105C0002. Opinions, interpretations,
conclusions and recommendations are those of the authors and are not
necessarily endorsed by the United States Government. M.C. and K.D. are
supported by Science Foundation Ireland Grant No. 11/PI/1177. 
Keywords: 
Bounds; inference; information theory; ratedistortion theory; 
Academic Unit: 
Faculty of Science and Engineering > Research Institutes > Hamilton Institute 
Item ID: 
5982 
Identification Number: 
arXiv:1310.1512 
Depositing User: 
Dr Ken Duffy

Date Deposited: 
24 Mar 2015 17:02 
Publisher: 
arXiv.org 
Refereed: 
Yes 
Funders: 
Intelligence Advanced Research Projects Activity, Science Foundation Ireland (SFI) 
URI: 

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