opendp::measures

Struct ZeroConcentratedDivergence

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pub struct ZeroConcentratedDivergence;
Expand description

Privacy measure used to define $\rho$-zero concentrated differential privacy.

In the following proof definition, $d$ corresponds to $\rho$ when also quantified over all adjacent datasets. That is, $\rho$ is the greatest possible $d$ over all pairs of adjacent datasets $x, x’$ where $Y \sim M(x)$, $Y’ \sim M(x’)$. $M(\cdot)$ is a measurement (commonly known as a mechanism). The measurement’s input metric defines the notion of adjacency, and the measurement’s input domain defines the set of possible datasets.

§Proof Definition

§d-closeness

For any two distributions $Y, Y’$ and any non-negative $d$, $Y, Y’$ are $d$-close under the zero-concentrated divergence measure if, for every possible choice of $\alpha \in (1, \infty)$,

D_\alpha(Y, Y') = \frac{1}{1 - \alpha} \mathbb{E}_{x \sim Y'} \Big[\ln \left( \dfrac{\Pr[Y = x]}{\Pr[Y' = x]} \right)^\alpha \Big] \leq d \cdot \alpha.

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impl ApproximateMeasure for ZeroConcentratedDivergence

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fn add_delta(_d_out: Self::Distance, _delta_p: f64) -> Fallible<Self::Distance>

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impl BasicCompositionMeasure for ZeroConcentratedDivergence

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fn concurrent(&self) -> Fallible<bool>

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fn compose(&self, d_i: Vec<Self::Distance>) -> Fallible<Self::Distance>

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impl Clone for ZeroConcentratedDivergence

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fn clone(&self) -> ZeroConcentratedDivergence

Returns a copy of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl ConcentratedMeasure for ZeroConcentratedDivergence

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type ApproxMeasure = SmoothedMaxDivergence

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fn convert( rho: Self::Distance, ) -> Fallible<<Self::ApproxMeasure as Measure>::Distance>

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impl Debug for ZeroConcentratedDivergence

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fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter. Read more
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impl Default for ZeroConcentratedDivergence

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fn default() -> ZeroConcentratedDivergence

Returns the “default value” for a type. Read more
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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for AtomDomain<i128>
where f64: InfCast<QI>,

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type InputMetric = AbsoluteDistance<QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for AtomDomain<i16>
where f64: InfCast<QI>,

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type InputMetric = AbsoluteDistance<QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for AtomDomain<i32>
where f64: InfCast<QI>,

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type InputMetric = AbsoluteDistance<QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for AtomDomain<i64>
where f64: InfCast<QI>,

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type InputMetric = AbsoluteDistance<QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for AtomDomain<i8>
where f64: InfCast<QI>,

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type InputMetric = AbsoluteDistance<QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for AtomDomain<isize>
where f64: InfCast<QI>,

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type InputMetric = AbsoluteDistance<QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for AtomDomain<u128>
where f64: InfCast<QI>,

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type InputMetric = AbsoluteDistance<QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for AtomDomain<u16>
where f64: InfCast<QI>,

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type InputMetric = AbsoluteDistance<QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for AtomDomain<u32>
where f64: InfCast<QI>,

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type InputMetric = AbsoluteDistance<QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for AtomDomain<u64>
where f64: InfCast<QI>,

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type InputMetric = AbsoluteDistance<QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for AtomDomain<u8>
where f64: InfCast<QI>,

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type InputMetric = AbsoluteDistance<QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for AtomDomain<usize>
where f64: InfCast<QI>,

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type InputMetric = AbsoluteDistance<QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for VectorDomain<AtomDomain<i128>>
where f64: InfCast<QI>,

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type InputMetric = LpDistance<2, QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for VectorDomain<AtomDomain<i16>>
where f64: InfCast<QI>,

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type InputMetric = LpDistance<2, QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for VectorDomain<AtomDomain<i32>>
where f64: InfCast<QI>,

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type InputMetric = LpDistance<2, QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for VectorDomain<AtomDomain<i64>>
where f64: InfCast<QI>,

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type InputMetric = LpDistance<2, QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for VectorDomain<AtomDomain<i8>>
where f64: InfCast<QI>,

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type InputMetric = LpDistance<2, QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for VectorDomain<AtomDomain<isize>>
where f64: InfCast<QI>,

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type InputMetric = LpDistance<2, QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for VectorDomain<AtomDomain<u128>>
where f64: InfCast<QI>,

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type InputMetric = LpDistance<2, QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for VectorDomain<AtomDomain<u16>>
where f64: InfCast<QI>,

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type InputMetric = LpDistance<2, QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for VectorDomain<AtomDomain<u32>>
where f64: InfCast<QI>,

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type InputMetric = LpDistance<2, QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for VectorDomain<AtomDomain<u64>>
where f64: InfCast<QI>,

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type InputMetric = LpDistance<2, QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for VectorDomain<AtomDomain<u8>>
where f64: InfCast<QI>,

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type InputMetric = LpDistance<2, QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<QI: Number> GaussianDomain<ZeroConcentratedDivergence, QI> for VectorDomain<AtomDomain<usize>>
where f64: InfCast<QI>,

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type InputMetric = LpDistance<2, QI>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl GaussianDomain<ZeroConcentratedDivergence, f32> for AtomDomain<f32>

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type InputMetric = AbsoluteDistance<f32>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl GaussianDomain<ZeroConcentratedDivergence, f32> for VectorDomain<AtomDomain<f32>>

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type InputMetric = LpDistance<2, f32>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl GaussianDomain<ZeroConcentratedDivergence, f64> for AtomDomain<f64>

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type InputMetric = AbsoluteDistance<f64>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl GaussianDomain<ZeroConcentratedDivergence, f64> for VectorDomain<AtomDomain<f64>>

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type InputMetric = LpDistance<2, f64>

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fn make_gaussian( input_domain: Self, input_metric: Self::InputMetric, scale: f64, k: Option<i32>, ) -> Fallible<Measurement<Self, Self::Carrier, Self::InputMetric, ZeroConcentratedDivergence>>

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impl<MI> GaussianMeasure<MI> for ZeroConcentratedDivergence
where MI: Metric, MI::Distance: Number, f64: InfCast<MI::Distance>,

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fn new_forward_map(scale: f64, relaxation: f64) -> PrivacyMap<MI, Self>

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impl Measure for ZeroConcentratedDivergence

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type Distance = f64

Proof Definition Read more
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impl NoiseExprMeasure for ZeroConcentratedDivergence

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const DISTRIBUTION: Distribution = Distribution::Gaussian

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type Metric = LpDistance<2, f64>

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fn map_function(scale: f64) -> impl Fn(&f64) -> Fallible<f64>

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impl PartialEq for ZeroConcentratedDivergence

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fn eq(&self, other: &ZeroConcentratedDivergence) -> bool

Tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<MS> PrivateDslPlan<MS, ZeroConcentratedDivergence> for DslPlan
where MS: 'static + UnboundedMetric, DslPlan: StableDslPlan<MS, MS>,

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fn make_private( self, input_domain: FrameDomain<DslPlan>, input_metric: MS, output_measure: ZeroConcentratedDivergence, global_scale: Option<f64>, threshold: Option<u32>, ) -> Fallible<Measurement<FrameDomain<DslPlan>, DslPlan, MS, ZeroConcentratedDivergence>>

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impl<M: 'static + UnboundedMetric> PrivateExpr<PartitionDistance<M>, ZeroConcentratedDivergence> for Expr

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fn make_private( self, input_domain: WildExprDomain, input_metric: PartitionDistance<M>, output_measure: ZeroConcentratedDivergence, global_scale: Option<f64>, ) -> Fallible<Measurement<WildExprDomain, ExprPlan, PartitionDistance<M>, ZeroConcentratedDivergence>>

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impl StructuralPartialEq for ZeroConcentratedDivergence

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impl<T> TryConv for T

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fn try_conv<T>(self) -> Result<T, Self::Error>
where Self: TryInto<T>,

Attempts to convert self into T using TryInto<T>. Read more
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<V, T> VZip<V> for T
where V: MultiLane<T>,

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fn vzip(self) -> V

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impl<T> Ungil for T
where T: Send,