Conference paper
Paper
Principal Inertia Components and Applications
Abstract
We explore properties and applications of the principal inertia components (PICs) between two discrete random variables and . The PICs lie in the intersection of information and estimation theory, and provide a fine-grained decomposition of the dependence between and . Moreover, the PICs describe which functions of can or cannot be reliably inferred (in terms of MMSE), given an observation of . 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.