Measurements

This section gives a high-level overview of the measurements that are available in the library. Refer to the section on measurements in the discussion of core structures for a defintion of “measurement” in OpenDP.

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
opendp.measurements.make_laplace()	VectorDomain<AtomDomain<T>>	L1Distance<T>	MaxDivergence

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
opendp.measurements.make_gaussian()	VectorDomain<AtomDomain<T>>	L2Distance<QI>	ZeroConcentratedDivergence

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

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
opendp.measurements.make_randomized_response()	AtomDomain<T>	DiscreteDistance	MaxDivergence