Amplification

If your dataset is a simple sample from a larger population, you can make the privacy relation more permissive by wrapping your measurement with a privacy amplification combinator: opendp.combinators.make_population_amplification().

Note

The amplifier requires a looser trust model, as the population size can be set arbitrarily.

>>> dp.enable_features("honest-but-curious")

In order to demonstrate this API, we’ll first create a measurement with a sized input domain. The resulting measurement expects the size of the input dataset to be 10.

Python

>>> atom_domain = dp.atom_domain(bounds=(0.0, 10.0), nan=False)
>>> input_space = (
...     dp.vector_domain(atom_domain, size=10),
...     dp.symmetric_distance(),
... )
>>> meas = (
...     input_space
...     >> dp.t.then_mean()
...     >> dp.m.then_laplace(scale=0.5)
... )
>>> print(
...     "standard mean:", meas([1.0] * 10)
... )  # -> 1.03 
standard mean: ...

We can now use the amplification combinator to construct an amplified measurement. The function on the amplified measurement is identical to the standard measurement.

Python

>>> amplified = dp.c.make_population_amplification(
...     meas, population_size=100
... )
>>> print(
...     "amplified mean:", amplified([1.0] * 10)
... )  # -> .97 
amplified mean: ...

The privacy relation on the amplified measurement takes into account that the input dataset of size 10 is a simple sample of individuals from a theoretical larger dataset that captures the entire population, with 100 rows.

Python

>>> # Where we once had a privacy utilization of ~2 epsilon...
>>> assert meas.check(2, 2.0 + 1e-6)
>>> # ...we now have a privacy utilization of ~.4941 epsilon.
>>> assert amplified.check(2, 0.4941)

The efficacy of this combinator improves as n gets larger.