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| -rw-r--r-- | posts/2019-03-13-a-tail-of-two-densities.md | 4 |
1 files changed, 2 insertions, 2 deletions
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 f3e409c..ba62777 100644 --- a/posts/2019-03-13-a-tail-of-two-densities.md +++ b/posts/2019-03-13-a-tail-of-two-densities.md @@ -340,7 +340,7 @@ As it turns out, **C3** is the condition we need. $(\epsilon, \delta)$-ind if and only if **C3** holds. **Proof**(Murtagh-Vadhan 2018). The \"if\" direction is proved -in the same way as Lemma 1. Without loss of generality we may assume +in the same way as Claim 1. Without loss of generality we may assume $\mathbb P(E) = \mathbb P(F) \ge 1 - \delta$. To see this, suppose $F$ has higher probability than $E$, then we can substitute $F$ with a subset of $F$ that has the same probability as $E$ (with possible @@ -506,7 +506,7 @@ $$\begin{aligned} \mathbb P(F_i | \xi_{\le i} = y_{\le i}) &= {f(y_{\le i}) \over q_i(y_{\le i})}. \end{aligned}$$ -The rest of the proof is almost the same as the proof of Lemma 2. +The rest of the proof is almost the same as the proof of Claim 4. $\square$ ### Back to approximate differential privacy |