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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),...
We consider the problem of diluting common randomness from correlated observations by separated agents. This problem creates a new framework to study statistical privacy, in which a legitimate party, Alice, has access to a random variable X, whereas an attacker, Bob, has access to a random variable Y dependent on X drawn from a joint distribution pX,Y. Alice's goal is to produce a non-trivial function...
We investigate the problem of intentionally disclosing information about a set of measurement points X (useful information), while guaranteeing that little or no information is revealed about a private variable S (private information). Given that S and X are drawn from a finite set with joint distribution pS,X, we prove that a non-trivial amount of useful information can be disclosed while not disclosing...
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