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authorYuchen Pei <me@ypei.me>2019-03-19 16:12:04 +0100
committerYuchen Pei <me@ypei.me>2019-03-19 16:12:04 +0100
commite07090c79b3907299ccfa42ea7949786d087c4d1 (patch)
tree2ebc7ded5fbb52e72c480af070487ce1fbc6ef12
parent802cd4cc4d78defa998250011440c5c41d87e4a0 (diff)
added some subsection
-rw-r--r--posts/2019-03-14-great-but-manageable-expectations.md4
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