Measurements#

This section gives a high-level overview of the measurements that are available in the library. Refer to the Measurement for an explanation of what a measurement is.

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:

Vector Input Metric

Constructor

L1Distance<T>

make_laplace

L2Distance<T>

make_gaussian

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.

Measurement

Input Domain

Input Metric

Output Measure

opendp.measurements.make_laplace()

AtomDomain<T>

AbsoluteDistance<T>

MaxDivergence<QO>

opendp.measurements.make_laplace()

VectorDomain<AtomDomain<T>>

L1Distance<T>

MaxDivergence<QO>

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

Input Domain

Input Metric

Output Measure

opendp.measurements.make_gaussian()

AtomDomain<T>

AbsoluteDistance<QI>

ZeroConcentratedDivergence<QO>

opendp.measurements.make_gaussian()

VectorDomain<AtomDomain<T>>

L2Distance<QI>

ZeroConcentratedDivergence<QO>

Geometric Noise#

The geometric mechanism (make_geometric) is an alias for the discrete Laplace (make_laplace). If you need constant-time execution to protect against timing side-channels, specify bounds!

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_laplace_threshold chains with.

See the Histograms notebook for code examples and more exposition.

Constructor

Input Domain

Input Metric

Output Metric/Measure

opendp.transformations.make_count_by()

VectorDomain<AtomDomain<TK>>

SymmetricDistance

L1Distance<TV>

opendp.measurements.make_laplace_threshold()

MapDomain<AtomDomain<TK>, AtomDomain<TV>>

L1Distance<TV>

SmoothedMaxDivergence<TV>

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.

Measurement

Input Domain

Input Metric

Output Measure

opendp.measurements.make_randomized_response_bool()

AtomDomain<bool>

DiscreteDistance

MaxDivergence<QO>

opendp.measurements.make_randomized_response()

AtomDomain<T>

DiscreteDistance

MaxDivergence<QO>