Differential privacy for dummies

The "dummies" are the authors of "Fool's Gold," to which this article is a rebuttal.

I also turned to Wikipedia immediately. Differential privacy is concerned with protecting individual records when making statistical queries. For example, if you could issue a query to a medical case database like »What proportion of the population was born on this specific date in that specific small town with some specific eye color and has this illness?« you could potentially figure out whether or not one person has a specific illness by either getting zero or a very small percentage. One possible solution and what is mostly discussed in the article is adding some noise to the result, as little as possible to not make the query result meaningless but enough to protect each record.

https://www.youtube.com/watch?v=5muBxGQ9B2g is a nice introduction and overview

Here is the basic idea of differential privacy in its simplest form.

Suppose that A is a eps-DP algorithm and X1, X2 are two datasets differing by a single point. Recall that for small eps, exp(eps) is roughly (1+eps) and exp(-eps) is roughly (1-eps), so eps-DP yields the guarantee that (roughly speaking), for all subsets S,

    (1-eps) * Pr{ A(X2) \in S } <= Pr{ A(X1) \in S } <= (1+eps) * Pr{ A(X2) \in S }. 

Intuitively speaking, the output distribution of A on X1 and X2 looks roughly the same, only differing by a factor (1 +/- eps), with a fudge factor eps that the user gets to control. Note that this is a very strong notion of stability of an algorithm.