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@ -163,11 +163,11 @@ In order to decrease the noise, we can use a differentially-private percentile t
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From [Differentially Private Marginals](./dp_marginals.pdf), to satisfy $(\varepsilon, \delta)$-DP, the following inequality needs to hold:
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(EQ1) $0.5 * R\varepsilon_Q^2 + 0.5 *\displaystyle\sum_{1}^{R} 1/\sigma_k^2 \leq (\sqrt{\varepsilon_M + \ln(2/\delta)} - \sqrt{\ln(2/\delta)})^2$, where the reported aggregate count is the $real\_aggregate\_count + \sigma_{k} * \sqrt{\Delta_k} * N(0, 1)$.
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(EQ1) $0.5 * R\varepsilon_Q^2 + 0.5 *\displaystyle\sum_{1}^{R} 1/\sigma_k^2 \leq (\sqrt{\varepsilon_M + \ln(2/\delta)} - \sqrt{\ln(2/\delta)})^2$, where the reported aggregate count is the `real_aggregate_count + ` $\sigma_{k} * \sqrt{\Delta_k} * N(0, 1)$.
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Assuming the total privacy budget to be $\varepsilon$, we then define:
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(EQ2) $\varepsilon = \varepsilon_M + \varepsilon_N$, where $\varepsilon_M$ is the portion of privacy budget we dedicate to the marginals EQ1 equation and $\varepsilon_N$ what we dedicate to protect the number of records - ($real\_number\_of\_records + Laplace(1 / \varepsilon_N)$).
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(EQ2) $\varepsilon = \varepsilon_M + \varepsilon_N$, where $\varepsilon_M$ is the portion of privacy budget we dedicate to the marginals EQ1 equation and $\varepsilon_N$ what we dedicate to protect the number of records - `real_number_of_records + ` $Laplace(1 / \varepsilon_N)$.
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Based on EQ1 and EQ2 we can:
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