Contraction of $E_\gamma$-Divergence and Its Applications to Privacy. (arXiv:2012.11035v2 [cs.IT] UPDATED)

We investigate the contraction coefficients derived from strong data
processing inequalities for the $E_\gamma$-divergence. By generalizing the
celebrated Dobrushin's coefficient from total variation distance to
$E_\gamma$-divergence, we derive a closed-form expression for the contraction
of $E_\gamma$-divergence. This result has fundamental consequences in two
privacy settings. First, it implies that local differential privacy can be
equivalently expressed in terms of the contraction of $E_\gamma$-divergence.
This equivalent formula can be used to precisely quantify the impact of local
privacy in (Bayesian and …

applications data data processing differential privacy local privacy privacy settings result settings terms