A mechanism is a randomized function that takes a data set as input
and returns a sample from a known probability distribution.
The mechanism is considered private if it can be proven to satisfy differential privacy.
Differentially private mechanisms are designed to convey useful information about the input data set.
This chapter formalizes and generalizes differentially private mechanisms.
Private mechanisms build on concepts discussed in Chapter 3,
like metric spaces, distance bounds, and stability.
These concepts form the foundation of a mathematically rigorous,
yet approachable, introduction to a variety of differentially private mechanisms.
Informally, differentially private mechanisms are similar in nature to transformations,
in that they transform data in a way that keeps outputs “close.”
However, the kind of closeness for mechanism output is different:
it is defined over the probabilities of the possible outputs.
The unifying perspective is that differential privacy is a system for relating distances.
Each query decomposes into a series of functions:
stable transformations followed by one private mechanism
and then zero or more postprocessors.
If you chain a transformation and mechanism,
or a mechanism and postprocessor, you get a new mechanism (see Figure 4-1).
Figure 4-1. A data processing pipeline from both the non-DP perspective and
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