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Diffstat (limited to 'posts')
| -rw-r--r-- | posts/2019-03-14-great-but-manageable-expectations.md | 4 |
1 files changed, 4 insertions, 0 deletions
diff --git a/posts/2019-03-14-great-but-manageable-expectations.md b/posts/2019-03-14-great-but-manageable-expectations.md index 554a7c4..d622fd4 100644 --- a/posts/2019-03-14-great-but-manageable-expectations.md +++ b/posts/2019-03-14-great-but-manageable-expectations.md @@ -156,6 +156,8 @@ the noise. However, as we will see later, compositions will yield different results from those obtained from methods in [Part 1](/posts/2019-03-13-a-tail-of-two-densities.html) when considering Rényi dp. +### Moment Composition + **Claim 22 (Moment Composition Theorem)**. Let $M$ be the adaptive composition of $M_{1 : k}$. Suppose for any $y_{< i}$, $M_i(y_{< i})$ is $(\lambda, \rho)$-rdp. Then $M$ is @@ -221,6 +223,8 @@ As we will see in the discussions at the end of this post, this result is different from (and probably better than) the one obtained by using the Advanced Composition Theorem (Claim 18). +### Subsampling + We also have a subsampling theorem for the Rényi dp. **Claim 24**. Fix $r \in [0, 1]$. Let $m \le n$ be two |