Measurements#
This section gives a high-level overview of the measurements that are available in the library. Refer to the Measurement section for an explanation of what a measurement is.
As mentioned in Getting Started, the intermediate domains and metrics need to match when chaining. This means you will need to choose a measurement that chains with your aggregator.
Additive Noise Mechanisms#
See the Additive Noise Mechanisms notebook for code examples and more exposition.
Notice that there is a symmetric structure to the additive noise measurements:
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In the following sections, scalar-valued and vector-valued versions of each measurement are listed separately.
You can choose whether to construct scalar or vector-valued versions by setting the D type argument when calling the constructor.
- Scalar:
D=AtomDomain[T](default)- Vector:
D=VectorDomain[AtomDomain[T]]
Laplacian Noise#
These algorithms accept sensitivities in terms of the absolute or L2 metrics and measure privacy in terms of epsilon.
Use the opendp.accuracy.laplacian_scale_to_accuracy() and opendp.accuracy.accuracy_to_laplacian_scale() functions to convert to/from accuracy estimates.
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There are more granular versions of these constructors, should you need them:
Expand Me
The primary constructors above switch between the cks20 and linear-time sampling algorithms depending on the noise scale. If the noise scale is greater than 10, the cks20 algorithm is more efficient. You can use these constructors to invoke the underlying algorithm directly. In addition, the linear-time algorithm supports a constant-time execution mode if noise bounds are passed.
Measurement |
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Gaussian Noise#
These algorithms accept sensitivities in terms of the absolute or L2 metrics and measure privacy in terms of rho (zero-concentrated differential privacy).
Use the opendp.accuracy.gaussian_scale_to_accuracy() and opendp.accuracy.accuracy_to_gaussian_scale() functions to convert to/from accuracy estimates.
Refer to Measure Casting to convert to approximate DP.
Measurement |
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Output Measure |
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Geometric Noise#
The geometric mechanism (make_base_geometric) is an alias for the discrete laplace (make_base_discrete_laplace).
If you need constant-time execution to protect against timing side-channels, use opendp.measurements.make_base_discrete_laplace_linear(), which is equivalent to the previous algorithm.
Noise Addition with Thresholding#
When releasing data grouped by an unknown key-set, it is necessary to use a mechanism that only releases keys which are “stable”. That is, keys which are present among all neighboring datasets.
The stability histogram is used to release a category set and frequency counts, and is useful when the category set is unknown or very large. make_count_by is included here because it is currently the only transformation that make_base_laplace_threshold chains with.
See the Histograms notebook for code examples and more exposition.
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Randomized Response#
These measurements are used to randomize an individual’s response to a query in the local-DP model.
See the Randomized Response notebook for code examples and more exposition.
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Bring Your Own#
Use opendp.measurements.make_user_measurement() to construct a measurement for your own mechanism.
Note
This requires a looser trust model, as we cannot verify any privacy or stability properties of user-defined functions.
>>> import opendp.prelude as dp
>>> dp.enable_features("honest-but-curious", "contrib")
This example mocks the typical API of the OpenDP library to make the most private DP mechanism ever!
>>> def make_base_constant(constant):
... """Constructs a Measurement that only returns a constant value."""
... def function(_arg: int):
... return constant
...
... def privacy_map(d_in: int) -> float:
... return 0.0
...
... return dp.m.make_user_measurement(
... input_domain=dp.atom_domain(T=int),
... input_metric=dp.absolute_distance(T=int),
... output_measure=dp.max_divergence(T=float),
... function=function,
... privacy_map=privacy_map,
... TO=type(constant), # the expected type of the output
... )
The resulting Measurement may be used interchangeably with those constructed via the library:
>>> meas = (
... (dp.vector_domain(dp.atom_domain((0, 10))), dp.symmetric_distance())
... >> dp.t.then_sum()
... >> make_base_constant("denied")
... )
...
>>> assert meas([2, 3, 4]) == "denied"
>>> assert meas.map(1) == 0. # computes epsilon, because the output measure is max divergence
While this mechanism clearly has no utility, the code snip may form a basis for you to create own measurements, or even incorporate mechanisms from other libraries.
You can also define your own transformations (opendp.transformations.make_user_transformation()) and postprocessors (opendp.core.new_function()).