Corrections to “Distribution Privacy Under Function Recoverability”
Ajaykrishnan Nageswaran, Prakash Narayan · IEEE Transactions on Information Theory · 2022
In the article[1], in the proof of Lemma 2, the sentence after (10) “For a fixed$Q^{(n)}$, since$(P_{X}W)^{n}(z^{n})$is the same for all$z^{n}\in \mathcal {T}_{Q^{(n)}}$, if$\widehat {P}_{n}(z^{n})$were to vary across$z^{n}\in \mathcal {T}_{Q^{(n)}}$, the querier can pick that$\tilde {z^{n}}$, say, in$\mathcal {T}_{Q^{(n)}}$for which$D\left ({P_{X}\big |\big |\widehat {P}_{n}\left ({\tilde {z^{n}}}\right)}\right)$is smallest over$\mathcal {T}_{Q^{(n)}}$and use$\widehat {P}_{n}\left ({\tilde {z^{n}}}\right)$as the estimate of$P_{X}$for all$z^{n}\in \mathcal {T}_{Q^{(n)}}$, denoting it by$\widehat {P}_{n}\left ({Q^{(n)}}\right)$; this will only serve to decrease the right-side of (10), bearing in mind the$\inf $with respect to$\widehat {P}_{n}$in the left-side of (5)” is incorrect.