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Fix bug in DP README.md (#1236)
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eriktaubeneck committed Aug 30, 2024
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7 changes: 3 additions & 4 deletions ipa-core/src/protocol/dp/README.md
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Expand Up @@ -8,10 +8,9 @@ introduces Binomials for DP.
considers their use for d-dimension queries (such as we will need for WALR).


To achieve a desired $(\varepsilon, \delta)$-DP guarantee, we generate $num_bernoulli$ secret shared samples of a
To achieve a desired $(\varepsilon, \delta)$-DP guarantee, we generate $num\\_bernoulli$ secret shared samples of a
Bernoulli having probability $0.5$ using PRSS. Next we aggregate them to get a Binomial sample. The result of the 2018
paper above is that for small epsilon (TODO, how small required?), we require the following number of samples
$$ num_bernoulli \geq 8 \log(2/\delta) /\varepsilon^2$$
paper above is that for small epsilon.

This [spreadsheet](https://docs.google.com/spreadsheets/d/1sMgqkMw3-yNBp6f8ctyv4Hdfx9Ei7muj0ZhP9i1DHrw/edit#gid=0)
looks at the calculation for different parameter choices and confirms that this approach does lead to a better final
Expand All @@ -22,4 +21,4 @@ Gaussians but the 2018 paper's analysis shows this).

## Binomial Noise for d-dimensional queries
For WALR we will be adding noise to a d-dimensional query, to add binomial noise we have to look
simulatenously at the sensitivity under three different norms, $\ell_1, \ell_2, \ell_\infty$. TODO.
simulatenously at the sensitivity under three different norms, $\ell_1, \ell_2, \ell_\infty$. TODO.

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