noise_mechanisms#
Measurements for adding noise to individual numbers.
Classes#
Add Laplace noise to a number. |
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Add Geometric noise to a number. |
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Add discrete Gaussian noise to a number. |
- class AddLaplaceNoise(input_domain, scale)#
Bases:
tmlt.core.measurements.base.MeasurementAdd Laplace noise to a number.
- Parameters
input_domain (Union[tmlt.core.domains.numpy_domains.NumpyIntegerDomain, tmlt.core.domains.numpy_domains.NumpyFloatDomain]) –
scale (tmlt.core.utils.exact_number.ExactNumberInput) –
- __init__(input_domain, scale)#
Constructor.
- Parameters
input_domain (
NumpyIntegerDomain|NumpyFloatDomainUnion[NumpyIntegerDomain,NumpyFloatDomain]) – Input Domain.scale (
ExactNumber|float|int|str|Fraction|ExprUnion[ExactNumber,float,int,str,Fraction,Expr]) – Noise scale.
- property input_domain(self)#
Return input domain for the measurement.
- Return type
- property scale(self)#
Returns the noise scale.
- Return type
- property output_type(self)#
Return the output data type after being used as a UDF.
- Return type
- privacy_function(self, d_in)#
Returns the smallest d_out satisfied by the measurement.
The returned d_out is \(\frac{d_{in}}{b}\) (\(\infty\) if \(b = 0\)).
where:
\(d_{in}\) is the input argument “d_in”
\(b\) is the property “scale”
- Parameters
d_in (tmlt.core.utils.exact_number.ExactNumberInput) – Distance between inputs under input_metric.
- Return type
- __call__(self, val)#
Returns the value with laplace noise added.
The added laplace noise has the probability density function
\(f(x) = \frac{1}{2 b} e ^ {\frac{-\mid x \mid}{b}}\)
where:
\(x\) is a real number
\(b\) is the property “scale”
- Parameters
val (Union[numpy.int32, numpy.int64, numpy.float32, numpy.float64]) – Value to add Laplace noise to.
- Return type
- property input_metric(self)#
Distance metric on input domain.
- Return type
- property output_measure(self)#
Distance measure on output.
- Return type
- privacy_relation(self, d_in, d_out)#
Return True if close inputs produce close outputs.
See the privacy and stability tutorial (add link?) for more information.
- Parameters
d_in (Any) – Distance between inputs under input_metric.
d_out (Any) – Distance between outputs under output_measure.
- Return type
- class AddGeometricNoise(alpha)#
Bases:
tmlt.core.measurements.base.MeasurementAdd Geometric noise to a number.
- Parameters
alpha (tmlt.core.utils.exact_number.ExactNumberInput) –
- __init__(alpha)#
Constructor.
- property input_domain(self)#
Return input domain for the measurement.
- property output_type(self)#
Return the output data type after being used as a UDF.
- Return type
- property alpha(self)#
Returns the noise scale.
- Return type
- privacy_function(self, d_in)#
Returns the smallest d_out satisfied by the measurement.
The returned d_out is \(\frac{d_{in}}{\alpha}\) (\(\infty\) if \(\alpha = 0\)).
where:
\(d_{in}\) is the input argument “d_in”
\(\alpha\) is
alpha
- Parameters
d_in (tmlt.core.utils.exact_number.ExactNumberInput) – Distance between inputs under input_metric.
- Return type
- __call__(self, value)#
Returns the value with double sided geometric noise added.
The added noise has the probability mass function
\[f(k)= \frac {e^{1 / \alpha} - 1} {e^{1 / \alpha} + 1} \cdot e^{\frac{-\mid k \mid}{\alpha}}\]where:
\(k\) is an integer
\(\alpha\) is
alpha
A double sided geometric distribution is the difference between two geometric distributions (It can be sampled from by sampling a two values from a geometric distribution, and taking their difference).
See section 4.1 in [BV18], remark 2 in this paper, or scipy.stats.geom for more information. (Note that the parameter \(p\) used in scipy.stats.geom is related to \(\alpha\) through \(p = 1 - e^{-1 / \alpha}\)).
- Parameters
value (Union[numpy.int32, numpy.int64]) – Value to add geometric noise to.
- Return type
- property input_metric(self)#
Distance metric on input domain.
- Return type
- property output_measure(self)#
Distance measure on output.
- Return type
- privacy_relation(self, d_in, d_out)#
Return True if close inputs produce close outputs.
See the privacy and stability tutorial (add link?) for more information.
- Parameters
d_in (Any) – Distance between inputs under input_metric.
d_out (Any) – Distance between outputs under output_measure.
- Return type
- class AddDiscreteGaussianNoise(sigma_squared)#
Bases:
tmlt.core.measurements.base.MeasurementAdd discrete Gaussian noise to a number.
- Parameters
sigma_squared (tmlt.core.utils.exact_number.ExactNumberInput) –
- __init__(sigma_squared)#
Constructor.
- property input_domain(self)#
Return input domain for the measurement.
- property output_type(self)#
Return the output data type after being used as a UDF.
- Return type
- property sigma_squared(self)#
Returns the noise scale.
- Return type
- privacy_function(self, d_in)#
Returns the smallest d_out satisfied by the measurement.
The returned d_out is \(\frac{d_{in}^2}{2 \cdot \sigma^2}\) (\(\infty\) if \(\sigma^2 = 0\)).
where:
\(d_{in}\) is the input argument “d_in”
\(\sigma^2\) is
sigma_squared
See Proposition 1.6 in this paper.
- Parameters
d_in (tmlt.core.utils.exact_number.ExactNumberInput) – Distance between inputs under input_metric.
- Return type
- __call__(self, value)#
Adds discrete Gaussian noise with specified scale.
The added noise has the probability mass function
\[f(k) = \frac {e^{k^2/2\sigma^2}} { \sum_{n\in \mathbb{Z}} e^{n^2/2\sigma^2} }\]where:
\(k\) is an integer
\(\sigma^2\) is
sigma_squared
See [CKS20] for more information. The formula above is based on Definition 1.
- Parameters
value (Union[numpy.int32, numpy.int64]) –
- Return type
- property input_metric(self)#
Distance metric on input domain.
- Return type
- property output_measure(self)#
Distance measure on output.
- Return type
- privacy_relation(self, d_in, d_out)#
Return True if close inputs produce close outputs.
See the privacy and stability tutorial (add link?) for more information.
- Parameters
d_in (Any) – Distance between inputs under input_metric.
d_out (Any) – Distance between outputs under output_measure.
- Return type