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Given a collection of real data, we want to do some statistical analysis.

For example, we take sum of them and reveal it to someone else.

But, we want to guarantee some sort of privacy of individual data.

In particular, suppose we have $(x_1, \ldots,x_n) \in \mathbb{R}^n$ and $a = \sum_i^n x_i$ is revealed to someone (not the individual value $x_i$). How can we measure or bound the leakage of each value $_$ from $$?

Does differential privacy help?

Carl
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mallea
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  • Since it was designed for solving statistical problems while preserving privacy: yes. Could you edit your question to make it more specific? – Tim Jun 14 '19 at 15:04
  • Thank you very much for your comment. Suppose we have $(x_1, \ldots, x_n) \in \mathbb{R}^n$ and $a = \sum_i^n x_i$ is revealed to someone (not the individual value). How can we measure or bound the leakage of each value $x_i$ from $a$? – mallea Jun 14 '19 at 15:17
  • This sounds like a different question that you asked. Maybe try editing it to give us more details and make it more precise? – Tim Jun 14 '19 at 15:23
  • @Tim I updated the queston – mallea Jun 14 '19 at 15:49
  • Answer: Maybe. The answer is case-wise specific. The concept of differential privacy was evolved from cryptography. In that context, privacy is defined as an absence of available decoding keys as well as a relative absence of information that can be decoded in the encrypted data. – Carl Jun 14 '19 at 19:27

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