The "Algorithmic Foundations of Differential Privacy" book (DOI: 10.1561/0400000042) introduces formally the "universe" and "database" on page 17 roughly as:
- $\mathcal{X}$ is a universe
- databases $x$ are collections of records from the universe
- For convenience, we use histogram of types from the universe $\mathcal{X}$ to represent $x$, such that: $x \in \mathbb{N}^{|\mathcal{X}|}$ where each entry $x_i$ represents the number of elements in the database $x$ of type $i \in \mathcal{X}$
If you take the example from Wikipedia
- The universe $\mathcal{X}$ is a set $\{0, 1\}$?
- The database $x$ is
- a vector
[3, 3]
(assuming the universe is ordered)? - or a map
{0:3, 1:3}
?
- a vector
My two questions are:
- Is my understanding correct?
- Why is it "convenient" to do so? What would be the non-convenient alternatives?