minor edits

2 files changed, 22 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 4897874..9f1c7a3 100644
--- a/posts/2019-03-13-a-tail-of-two-densities.md
+++ b/posts/2019-03-13-a-tail-of-two-densities.md
@@ -51,7 +51,8 @@ Vadhan, Jonathan Ullman, Yuanyuan Xu and Yiting Li for communication and
 discussions. The research was done while working at [KTH Department of
 Mathematics](https://www.kth.se/en/sci/institutioner/math).
 
-*This post is licensed under [CC BY-SA](https://creativecommons.org/licenses/by-sa/4.0/)
+*This post (including both Part 1 and Part2) is licensed under 
+[CC BY-SA](https://creativecommons.org/licenses/by-sa/4.0/)
 and [GNU FDL](https://www.gnu.org/licenses/fdl.html).*
 
 The gist of differential privacy 
diff --git a/posts/2019-03-14-great-but-manageable-expectations.md b/posts/2019-03-14-great-but-manageable-expectations.md
index 578bb09..2ec280a 100644
--- a/posts/2019-03-14-great-but-manageable-expectations.md
+++ b/posts/2019-03-14-great-but-manageable-expectations.md
@@ -5,7 +5,26 @@ template: post
 comments: true
 ---
 
-Let us continue with the study of differential privacy from [Part 1 of this post](/posts/2019-03-13-a-tail-of-two-densities.html).
+This is Part 2 of a two-part blog post on differential privacy.
+Continuing from [Part 1](/posts/2019-03-13-a-tail-of-two-densities.html),
+I discuss the Rényi differential privacy, corresponding to
+the Rényi divergence, a study of the moment generating functions the 
+divergence between probability measures to derive the tail bounds. 
+
+Like in Part 1, I prove a composition theorem and a subsampling theorem.
+
+I also attempt to reproduce a seemingly better moment bound for the
+Gaussian mechanism with subsampling, with one intermediate step which I
+am not able to prove.
+
+After that I explain the Tensorflow implementation of differential privacy,
+which focuses on the differentially private stochastic gradient descent 
+algorithm (DP-SGD).
+
+Finally I use the results from both Part 1 and Part 2 to obtain some privacy
+guarantees for composed subsampling queries in general, and for DP-SGD in particular. 
+I also compare these privacy guarantees.
+
 
 Rényi divergence and differential privacy 
 -----------------------------------------