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Diffstat (limited to 'posts/2019-03-14-great-but-manageable-expectations.md')
| -rw-r--r-- | posts/2019-03-14-great-but-manageable-expectations.md | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/posts/2019-03-14-great-but-manageable-expectations.md b/posts/2019-03-14-great-but-manageable-expectations.md index be7bf81..39c3487 100644 --- a/posts/2019-03-14-great-but-manageable-expectations.md +++ b/posts/2019-03-14-great-but-manageable-expectations.md @@ -215,7 +215,7 @@ $(\lambda, {1 \over \lambda - 1} \log (1 + r(e^{(\lambda - 1) \rho} - 1)))$-rdp. To prove Claim 24, we need a useful lemma: -{#Claim 25}**Claim 25**. Let $p_{1 : n}$ and $q_{1 : n}$ be +**Claim 25**. Let $p_{1 : n}$ and $q_{1 : n}$ be nonnegative integers, and $\lambda > 1$. Then $${(\sum p_i)^\lambda \over (\sum q_i)^{\lambda - 1}} \le \sum_i {p_i^\lambda \over q_i^{\lambda - 1}}. \qquad (8)$$ @@ -546,9 +546,9 @@ least when $\lambda$ is an integer. decode how `_compute_log_a_frac` computes the cumulant (or an upper bound of it) in this case - The function `_compute_delta` computes $\delta$s for a list of - $\lambda$s and $\kappa$s using Item 1 of Claim 3 and return the + $\lambda$s and $\kappa$s using Item 1 of Claim 25 and return the smallest one, and the function `_compute_epsilon` computes epsilon - uses Item 3 in the same way. + uses Item 3 in Claim 25 in the same way. In `optimizers`, among other things, the DP-SGD with Gaussian mechanism is implemented in `dp_optimizer.py` and `gaussian_query.py`. See the |