public abstract class ImmutablePairDistributionBase<TElement1, TElementDistribution1, TElement2, TElementDistribution2, TThis> : IImmutableDistribution<(Option<TElement1>, Option<TElement2>), TThis>, IImmutableDistribution, ICloneable, Diffable, CanCreateUniform<TThis>, CanCreatePointMass<(Option<TElement1>, Option<TElement2>), TThis>, CanGetLogProb<(Option<TElement1>, Option<TElement2>)>, CanGetLogAverageOf<TThis>, CanComputeProduct<TThis>, CanComputeProduct<TThis, TThis>, SummableExactly<TThis>, SummableExactly<TThis, TThis>, Summable<TThis, TThis>, CanCreatePartialUniform<TThis> where TElementDistribution1 : IImmutableDistribution<TElement1, TElementDistribution1>, CanGetLogAverageOf<TElementDistribution1>, CanComputeProduct<TElementDistribution1>, CanCreatePartialUniform<TElementDistribution1>, new()
    where TElementDistribution2 : IImmutableDistribution<TElement2, TElementDistribution2>, CanGetLogAverageOf<TElementDistribution2>, CanComputeProduct<TElementDistribution2>, CanCreatePartialUniform<TElementDistribution2>, new()
    where TThis : ImmutablePairDistributionBase<TElement1, TElementDistribution1, TElement2, TElementDistribution2, TThis>, new()

Type Parameters

Name	Description
TElement1	The type of a first element of a pair.
TElementDistribution1	The type of a distribution over `TElement1`.
TElement2	The type of a second element of a pair.
TElementDistribution2	The type of a distribution over `TElement2`.
TThis	The type of a concrete pair distribution class.

Remarks

Default interface implementations available in this class assume that the distribution is fully factorized: P(x, y) = P(x) P(y), where P(x) is given by First and P(y) is given by second. Implementations of another kinds of pair distributions must override the interface implementation to ensure the correct behavior.

One of the element distributions can be null to encode an epsilon input or an epsilon output in a transducer. Both distributions cannot be null at the same time: epsilon transition in transducers are specified by setting pair distributions to null.

Fields

ElementDistribution1Factory

Declaration

protected static readonly TElementDistribution1 ElementDistribution1Factory

Field Value

Type	Description
TElementDistribution1

ElementDistribution2Factory

Declaration

protected static readonly TElementDistribution2 ElementDistribution2Factory

Field Value

Type	Description
TElementDistribution2

Properties

First

Gets or sets the marginal distribution over the first element in a pair.

Declaration

public Option<TElementDistribution1> First { get; protected set; }

Property Value

Type	Description
Option<TElementDistribution1>

IsPointMass

Gets whether the distribution parameters represent a point mass.

Declaration

public bool IsPointMass { get; }

Property Value

Type	Description
Boolean

Point

Gets the point mass represented by the distribution.

Declaration

public virtual (Option<TElement1>, Option<TElement2>) Point { get; }

Property Value

Type	Description
(T1, T2)<Option<TElement1>, Option<TElement2>>

Second

Gets or sets the marginal distribution over the second element in a pair.

Declaration

public Option<TElementDistribution2> Second { get; protected set; }

Property Value

Type	Description
Option<TElementDistribution2>

Methods

Clone()

Creates a copy of the current distribution.

Declaration

public virtual object Clone()

Returns

Type	Description
Object	The created copy.

CreatePartialUniform()

Creates a distribution uniform over the support of the current distribution.

Declaration

public virtual TThis CreatePartialUniform()

Returns

Type	Description
TThis	The created distribution.

CreatePointMass((Option<TElement1>, Option<TElement2>))

Creates a point mass distribution.

Declaration

public virtual TThis CreatePointMass((Option<TElement1>, Option<TElement2>) point)

Parameters

Type	Name	Description
(T1, T2)<Option<TElement1>, Option<TElement2>>	point

Returns

Type	Description
TThis	The created distribution.

CreateUniform()

Creates a uniform distribution

Declaration

public virtual TThis CreateUniform()

Returns

Type	Description
TThis	The created distribution.

FromFirst(Option<TElementDistribution1>)

Creates a pair distribution for an epsilon output transducer transition.

Declaration

public static TThis FromFirst(Option<TElementDistribution1> first)

Parameters

Type	Name	Description
Option<TElementDistribution1>	first	The element distribution to weight the input element.

Returns

Type	Description
TThis	The created distribution.

FromFirstSecond(Option<TElementDistribution1>, Option<TElementDistribution2>)

Creates a pair distribution for a transducer transition.

Declaration

public static TThis FromFirstSecond(Option<TElementDistribution1> first, Option<TElementDistribution2> second)

Parameters

Type	Name	Description
Option<TElementDistribution1>	first	The element distribution to weight the input element.
Option<TElementDistribution2>	second	The element distribution to weight the output element.

Returns

Type	Description
TThis	The created distribution.

Remarks

One of first and second can be null to encode an epsilon input or an epsilon output transducer transition, but not both.

FromSecond(Option<TElementDistribution2>)

Creates a pair distribution for an epsilon input transducer transition.

Declaration

public static TThis FromSecond(Option<TElementDistribution2> second)

Parameters

Type	Name	Description
Option<TElementDistribution2>	second	The element distribution to weight the output element.

Returns

Type	Description
TThis	The created distribution.

GetLogAverageOf(TThis)

The log-probability that two distributions would draw the same sample.

Declaration

public virtual double GetLogAverageOf(TThis that)

Parameters

Type	Name	Description
TThis	that

Returns

Type	Description
Double	`Math.Log(sum_x this.Evaluate(x)*that.Evaluate(x))`

Remarks

This can be considered a type of inner product between distributions.

GetLogProb((Option<TElement1>, Option<TElement2>))

Evaluate the log of the density function at the specified domain value

Declaration

public abstract double GetLogProb((Option<TElement1>, Option<TElement2>) pair)

Parameters

Type	Name	Description
(T1, T2)<Option<TElement1>, Option<TElement2>>	pair

Returns

Type	Description
Double	The log density

IsPartialUniform()

Checks whether the distribution is uniform over its support.

Declaration

public virtual bool IsPartialUniform()

Returns

Type	Description
Boolean	true if the distribution is uniform over its support, false otherwise.

IsUniform()

Checks whether the current distribution is uniform.

Declaration

public virtual bool IsUniform()

Returns

Type	Description
Boolean	true if the current distribution is uniform, false otherwise.

MaxDiff(Object)

The maximum difference between this instance and the given

Declaration

public abstract double MaxDiff(object that)

Parameters

Type	Name	Description
Object	that

Returns

Type	Description
Double

Multiply(TThis)

Computes the product of the current instance and other.

Declaration

public abstract TThis Multiply(TThis other)

Parameters

Type	Name	Description
TThis	other

Returns

Type	Description
TThis	The product.

ProjectFirst(TElement1, out Option<TElementDistribution2>)

Computes P(y) = R(x, y), where R(x, y) is the current pair distribution, and x is a given element.

Declaration

public virtual double ProjectFirst(TElement1 first, out Option<TElementDistribution2> result)

Parameters

Type	Name	Description
TElement1	first	The element to project.
Option<TElementDistribution2>	result	The normalized projection result.

Returns

Type	Description
Double	The logarithm of the scale for the projection result.

ProjectFirst(TElementDistribution1, out Option<TElementDistribution2>)

Computes P(y) = sum_x Q(x) R(x, y), where R(x, y) is the current pair distribution, and Q(x) is a given element distribution.

Declaration

public virtual double ProjectFirst(TElementDistribution1 first, out Option<TElementDistribution2> result)

Parameters

Type	Name	Description
TElementDistribution1	first	The element distribution to project.
Option<TElementDistribution2>	result	The normalized projection result.

Returns

Type	Description
Double	The logarithm of the scale for the projection result.

Sum(Double, TThis, Double)

Computes a distribution with its parameters set to best match a mixture distribution.

Declaration

public abstract TThis Sum(double weightThis, TThis other, double weightOther)

Parameters

Type	Name	Description
Double	weightThis	A finite nonnegative weight.
TThis	other
Double	weightOther	A finite nonnegative weight.

Returns

Type	Description
TThis	A distribution of the result type that best matches a mixture distribution.

ToString()

Returns a string that represents the distribution.

Declaration

public override string ToString()

Returns

Type	Description
String	A string that represents the distribution.

Overrides

Object.ToString()

Implements

IImmutableDistribution<T, TThis>

IImmutableDistribution

System.ICloneable

Diffable

CanCreateUniform<TDist>

CanCreatePointMass<T, TDist>

CanGetLogProb<T>

CanGetLogAverageOf<T>

CanComputeProduct<T>

CanComputeProduct<TOther, TResult>

SummableExactly<T>

SummableExactly<TOther, TResult>

Summable<TOther, TResult>

CanCreatePartialUniform<TDist>