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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 e71651a..6467a5f 100644 --- a/posts/2019-03-13-a-tail-of-two-densities.md +++ b/posts/2019-03-13-a-tail-of-two-densities.md @@ -132,12 +132,12 @@ $$\mathbb P(M(x) \in S) \le e^\epsilon P(M(x') \in S). \qquad (1)$$ An example of $\epsilon$-dp mechanism is the Laplace mechanism. -**Definition**. The Laplace distribution over $\mathbb R$ +**Definition**. The *Laplace distribution* over $\mathbb R$ with parameter $b > 0$ has probability density function $$f_{\text{Lap}(b)}(x) = {1 \over 2 b} e^{- {|x| \over b}}.$$ -**Definition**. Let $d = 1$. The Laplace mechanism is +**Definition**. Let $d = 1$. The *Laplace mechanism* is defined by $$M(x) = f(x) + \text{Lap}(b).$$ |