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martinthomson committed Jul 24, 2024
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16 changes: 8 additions & 8 deletions draft-case-ppm-binomial-dp.md
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Expand Up @@ -203,12 +203,12 @@ sensitivity, {{compute-n}} describes how to determine the number of Bernoulli
samples needed.

To count the number of successes across these `N` trials, the MPC helpers simply
run an aggregation circuit over the secret shared results of the `N` Bernoulli
trials, each or which is either 0 or 1. The result of this sum is a sample from
a `Bin(N, p)` distribution. This binomial noise value is then added to the
output inside the MPC and then the final noised result revealed to the
appropriate output parties. That is, if the MPC computes `f(D)`, it outputs
shares of the result `f(D) + Bin(N,p)`.
add the secret shared results of the `N` Bernoulli trials, each or which is
either 0 or 1. The result of this sum is a sample from a `Bin(N, p)`
distribution. This binomial noise value is then added to the output inside the
MPC and then the final noised result revealed to the appropriate output parties.
That is, if the MPC computes `f(D)`, it outputs shares of the result `f(D) +
Bin(N,p)`.

The party receiving the output can then postprocess this output to get an
unbiased estimate for `f(D)` by subtracting the mean of the `Bin(N,p)`
Expand Down Expand Up @@ -264,7 +264,7 @@ o = f(D) / s + X
For an MPC system, the output of the system is shares of this scaled and biased
value. The recipient can reconstruct the an unbiased, unscaled, noised value by:

* Adding the shares it receives: `o = sum(o_i, o_2, …)`
* Adding the shares it receives: `o = sum(o_1, o_2, …)`
* Correcting for bias: `o - N\*p`
* Scaling the value: `f′(D) = s * (o - N\*p)`

Expand Down Expand Up @@ -299,7 +299,7 @@ For `f(D)` that produces output that is a `d`-dimensional vector of integer
values, the `p`-norms of interest for use with the binomial mechanism is the L1,
L2, and L∞ (or Linfty) norms.

The L1 norm of `x∊ℤ<sup>d</sup>` is:
The L1 norm of `x` (where x∊ℤ<sup>d</sup>) is:

~~~ pseudocode
sensitivity\_1 = ||x||<sub>1</sub> = sum(i=1..d, |x_i|)
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