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authorYuchen Pei <me@ypei.me>2019-03-25 15:22:55 +0100
committerYuchen Pei <me@ypei.me>2019-03-25 15:22:55 +0100
commit68713c9d8913a1b39e3690dd69f50c002872e110 (patch)
tree43353192103d1e0b424e96a8d1738b3036e3501f
parentfeaed25331619aa7acdc82dde7c4193fca4a6d44 (diff)
minor
-rw-r--r--posts/2019-03-13-a-tail-of-two-densities.md6
1 files changed, 3 insertions, 3 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 a096b25..41a3b57 100644
--- a/posts/2019-03-13-a-tail-of-two-densities.md
+++ b/posts/2019-03-13-a-tail-of-two-densities.md
@@ -934,8 +934,8 @@ $$D(p || q) = \mathbb E_{\xi \sim p} \log {p(\xi) \over q(\xi)} \le \max_y {\log
Comparing the quantity in Claim 11 ($\epsilon(e^\epsilon - 1)$) with the
quantity above ($\epsilon$), we arrive at the conclusion. $\square$
-**Claim 13 (Hoeffding\'s
-Inequality)**. Let $L_i$ be independent random variables with
+**Claim 13 ([Hoeffding\'s Inequality](https://en.wikipedia.org/wiki/Hoeffding%27s_inequality))**.
+Let $L_i$ be independent random variables with
$|L_i| \le b$, and let $L = L_1 + ... + L_k$, then for $t > 0$,
$$\mathbb P(L - \mathbb E L \ge t) \le \exp(- {t^2 \over 2 k b^2}).$$
@@ -981,7 +981,7 @@ $$\mathbb P(L(q || p) \le k a(\epsilon) + \sqrt{2 k \epsilon^2 \log \beta^{-1}})
By Claim 1 we arrive at the conclusion. $\square$
-**Claim 15 (Azuma\'s Inequality)**.
+**Claim 15 ([Azuma\'s Inequality](https://en.wikipedia.org/wiki/Azuma%27s_inequality))**.
Let $X_{0 : k}$ be a [supermartingale](https://en.wikipedia.org/wiki/Martingale_(probability_theory)).
If $|X_i - X_{i - 1}| \le b$, then