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| -rw-r--r-- | posts/2019-03-13-a-tail-of-two-densities.md | 4 |
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diff --git a/posts/2019-03-13-a-tail-of-two-densities.md b/posts/2019-03-13-a-tail-of-two-densities.md index fbf3127..f7740e2 100644 --- a/posts/2019-03-13-a-tail-of-two-densities.md +++ b/posts/2019-03-13-a-tail-of-two-densities.md @@ -918,6 +918,10 @@ when $\epsilon$ is sufficiently small, in which case the leading term is of orde $O(\sqrt k \epsilon)$ and we save a $\sqrt k$ in the $\epsilon$-part compared to the Basic Composition Theorem (Claim 10). +**Remark**. In practice one can try different choices of $\beta$ and settle +with the one that gives the best privacy guarantee. +See the discussions at the end of Part 2 of this post. + **Proof**. Let $p_i$, $q_i$, $p$ and $q$ be the laws of $M_i(x)$, $M_i(x')$, $M(x)$ and $M(x')$ respectively. |