Principal inertia components and applications
Files
First author draft
Date
2017-08-01
Authors
Calmon, Flavio du Pin
Makhdoumi, A.
Medard, M.
Varia, Mayank
Christiansen, M.
Duffy, K.R.
Version
First author draft
OA Version
Citation
F.D.P. Calmon, A. Makhdoumi, M. Medard, M. Varia, M. Christiansen, K.R. Duffy. 2017. "Principal Inertia Components and Applications." IEEE TRANSACTIONS ON INFORMATION THEORY. https://doi.org/10.1109/TIT.2017.2700857
Abstract
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.