Principal Inertia Components and Applications
Name
1704.00820.pdf
Description
Submitted version
Size
848.83 KB
Format
Adobe PDF
Checksum (MD5)
1f89c519750546c77983c4c69bc54268
Author(s)
Calmon, Flavio du Pin
Makhdoumi, Ali
Medard, Muriel
Varia, Mayank
Christiansen, Mark
Duffy, Ken R
Date Issued
2017
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Version
Original manuscript
Abstract
© 1963-2012 IEEE. We explore properties and applications of the principal inertia components (PICs) between two discrete random variables $X$ and $Y$. The PICs lie in the intersection of information and estimation theory, and provide a fine-grained decomposition of the dependence between $X$ and $Y$. Moreover, the PICs describe which functions of $X$ can or cannot be reliably inferred (in terms of MMSE), given an observation of $Y$. We demonstrate that the PICs play an important role in information theory, and they can be used to characterize information-theoretic limits of certain estimation problems. In privacy settings, we prove that the PICs are related to the fundamental limits of perfect privacy.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/TIT.2017.2700857
