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
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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.
DepartmentLincoln 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
Proceedings of the 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Institute of Electrical and Electronics Engineers (IEEE)
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).
Author's final manuscript