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arXiv · 1704.00820

Principal Inertia Components and Applications

Flavio P. Calmon·Ali Makhdoumi·Muriel Médard·Mayank Varia·Mark Christiansen·Ken R. Duffy
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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 fundamental limits of perfect privacy.

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Flavio P. Calmon, Ali Makhdoumi, Muriel Médard, Mayank Varia, Mark Christiansen, Ken R. Duffy. 2017-04-03. Principal Inertia Components and Applications. https://arxiv.org/abs/1704.00820

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