Core Structures

(See also opendp.core in the API reference.)

OpenDP is focused on creating computations with specific privacy characteristics. These computations are modeled with two core structures in OpenDP: opendp.mod.Transformation and opendp.mod.Measurement. These structures are in all OpenDP programs, regardless of the underlying algorithm or definition of privacy. By modeling computations in this way, we’re able to combine them in flexible arrangements and reason about the privacy properties of the resulting programs. OpenDP relates:

1. an upper bound on distance between function inputs to:

2. an upper bound on distance between respective function outputs (or output distributions)

Each transformation or measurement is a self-contained structure defined by a function that operates on values, and a map that operates on domains.

Similarities

Both transformations and measurements are mappings from inputs to outputs, and they share these four fields:

input_domain:

A domain that describes the set of all possible input values for the function.

output_domain:

A domain that describes the set of all possible output values of the function.

function:

A function that transforms data.

input_metric:

A metric used to compute distance between two members of the input domain.

Transformations and measurements have two additional fields, and this is where they differ:

Transformation	Measurement
output_metric	output_measure
stability_map	privacy_map

Transformation

A Transformation is a deterministic mapping from datasets to datasets. Transformations are used to preprocess and aggregate data.

Let’s assume we have a transformation called trans:

output = trans(input)
d_out = trans.map(d_in)

The tranformation trans can be called as if it were a function: this just evaluates the function field. We’ll say that “trans is (d_in, d_out)-stable” if outputs of trans are d_out-close when inputs are d_in-close.

The distances d_in and d_out are expressed in the units of the input metric and output metric. Depending on the context, d_in and d_out could be a distance bound to neighboring datasets or a global sensitivity. More information on distances is available here.

Invoking the function transforms the data, but the output is not differentially private. Transformations need to be chained with a measurement before they can be used to create a differentially-private release.

Measurement

(See also opendp.measurements in the API reference.)

A Measurement is, in contrast, a randomized mapping from datasets to outputs. Measurements are used to create differentially private releases.

Say we have an arbitrary instance of a Measurement, called meas, and a code snippet:

output = meas(input)
d_out = meas.map(d_in)

This should look familiar!

However, instead of talking about stability, we’ll say that “meas is (d_in, d_out)-differentially private” if outputs of meas are d_out-close when inputs are d_in-close.

The distances d_in and d_out are expressed in the units of the input metric and output measure, rather than metric. Because measurements emit samples from a probability distribution, a measure is used to quantify differences between probability distributions.

Depending on the context, d_in could be a distance bound to neighboring datasets or a global sensitivity, and d_out may be epsilon, (epsilon, delta), or some other measure of privacy.