chaining

Measurements constructed by chaining other measurements and transformations.

Classes

ChainTM

Measurement constructed by chaining a transformation and a measurement.

class ChainTM(transformation, measurement, hint=None)

Bases: tmlt.core.measurements.base.Measurement

Measurement constructed by chaining a transformation and a measurement.

Parameters

• transformation (tmlt.core.transformations.base.Transformation) –

• measurement (tmlt.core.measurements.base.Measurement) –

• hint (Optional[Callable[[Any, Any], Any]]) –

__init__(transformation, measurement, hint=None)

Constructor.

Parameters

• transformation (TransformationTransformation) – Transformation component (called first).

• measurement (MeasurementMeasurement) – Measurement component (called second).

• hint ((Any, Any) → Any | NoneOptional[Callable[[Any, Any], Any]] (default: None)) – An optional function to compute the intermediate metric value (after the transformation, but before the measurement) for privacy_relation(). It takes in the same inputs as privacy_relation(), and is only required if the transformation’s stability_function() raises NotImplementedError.

property measurement

Returns measurement being chained.

Return type

tmlt.core.measurements.base.Measurement

property transformation

Returns transformation being chained.

Return type

tmlt.core.transformations.base.Transformation

privacy_function(d_in)

Returns the smallest d_out satisfied by the measurement.

Returns M.privacy_function(T.stability_function(d_in)).

where:

• T is the transformation applied (transformation”)

• M is the measurement applied (measurement”)

Parameters

d_in (Any) – Distance between inputs under input_metric.

Raises

NotImplementedError – If M.privacy_function(T.stability_function(d_in)) raises NotImplementedError.

Return type

Any

privacy_relation(d_in, d_out)

Returns True only if outputs are close under close inputs.

Let d_mid = T.stability_function(d_in), or hint(d_in, d_out) if T.stability_function raises NotImplementedError.

This returns True only if the following hold:

1. T.stability_relation(d_in, d_mid)

2. M.privacy_relation(d_mid, d_out)

where:

• T is the transformation applied (transformation”)

• M is the measurement applied (measurement”)

• hint is the hint passed to the constructor.

Parameters

• d_in (Any) – Distance between inputs under input_metric.

• d_out (Any) – Distance between outputs under output_measure.

Raises

ValueError – If a hint is not provided and T.stability_function raises NotImplementedError.

Return type

bool

__call__(data)

Computes measurement after applying transformation on input data.

Parameters

data (Any) –

Return type

Any

property input_domain

Return input domain for the measurement.

Return type

tmlt.core.domains.base.Domain

property input_metric

Distance metric on input domain.

Return type

tmlt.core.metrics.Metric

property output_measure

Distance measure on output.

Return type

tmlt.core.measures.Measure

property is_interactive

Returns true iff the measurement is interactive.

Return type

bool