Struct TruncatedGaussian

A distribution over real numbers between an upper and lower bound. If both bounds are infinite, it reduces to an ordinary Gaussian distribution.

Inherited Members
Namespace: Microsoft.ML.Probabilistic.Distributions
Assembly: Microsoft.ML.Probabilistic.dll
Syntax
[Serializable]
[DataContract]
[Quality(QualityBand.Preview)]
public struct TruncatedGaussian : IDistribution<double>, IDistribution, ICloneable, HasPoint<double>, CanGetLogProb<double>, SettableTo<TruncatedGaussian>, Diffable, SettableToProduct<TruncatedGaussian>, SettableToProduct<TruncatedGaussian, TruncatedGaussian>, SettableToUniform, SettableToRatio<TruncatedGaussian>, SettableToRatio<TruncatedGaussian, TruncatedGaussian>, SettableToPower<TruncatedGaussian>, Sampleable<double>, SettableToWeightedSum<TruncatedGaussian>, CanGetMean<double>, CanGetVariance<double>, CanGetMeanAndVarianceOut<double, double>, CanGetLogNormalizer, CanGetLogAverageOf<TruncatedGaussian>, CanGetLogAverageOfPower<TruncatedGaussian>, CanGetAverageLog<TruncatedGaussian>, ITruncatableDistribution<double>, CanGetProbLessThan<double>, CanGetQuantile<double>
Remarks

The distribution is parameterized by a Gaussian and two real numbers (LowerBound, UpperBound). Between the bounds, the density is proportional to the Gaussian. Outside of the bounds, the density is zero.

Constructors

TruncatedGaussian(Gaussian)

Create a truncated Gaussian equivalent to a Gaussian, i.e. with no truncation.

Declaration
public TruncatedGaussian(Gaussian that)
Parameters
Type Name Description
Gaussian that

TruncatedGaussian(Gaussian, Double, Double)

Create a truncated Gaussian from a Gaussian and bounds

Declaration
[Construction(new string[]{"Gaussian", "LowerBound", "UpperBound"})]
public TruncatedGaussian(Gaussian gaussian, double lowerBound, double upperBound)
Parameters
Type Name Description
Gaussian gaussian
Double lowerBound
Double upperBound

TruncatedGaussian(TruncatedGaussian)

Create a new TruncatedGaussian distribution equal to that

Declaration
public TruncatedGaussian(TruncatedGaussian that)
Parameters
Type Name Description
TruncatedGaussian that

TruncatedGaussian(Double, Double, Double, Double)

Create a truncated Gaussian from untruncated (mean, variance) and bounds

Declaration
public TruncatedGaussian(double mean, double variance, double lowerBound, double upperBound)
Parameters
Type Name Description
Double mean
Double variance
Double lowerBound
Double upperBound

Fields

Gaussian

Untruncated Gaussian

Declaration
[DataMember]
public Gaussian Gaussian
Field Value
Type Description
Gaussian

LowerBound

Lower bound

Declaration
[DataMember]
public double LowerBound
Field Value
Type Description
Double

UpperBound

Upper bound

Declaration
[DataMember]
public double UpperBound
Field Value
Type Description
Double

Properties

IsPointMass

True if the distribution is a point mass.

Declaration
[IgnoreDataMember]
public readonly bool IsPointMass { get; }
Property Value
Type Description
Boolean

Point

Set this distribution to a point mass, or get its location

Declaration
[IgnoreDataMember]
public double Point { get; set; }
Property Value
Type Description
Double

Methods

Clone()

Make a deep copy of this distribution.

Declaration
public object Clone()
Returns
Type Description
Object

Equals(Object)

True if this distribution has the same parameters as that

Declaration
public override bool Equals(object thatd)
Parameters
Type Name Description
Object thatd

The instance to compare to
Returns
Type Description
Boolean
Overrides

FromGaussian(Gaussian)

Create a truncated Gaussian equivalent to a Gaussian, i.e. with no truncation.

Declaration
public static TruncatedGaussian FromGaussian(Gaussian gaussian)
Parameters
Type Name Description
Gaussian gaussian
Returns
Type Description
TruncatedGaussian

GetAverageLog(TruncatedGaussian)

Get the average logarithm of that distribution under this distribution, i.e. int this(x) log( that(x) ) dx

Declaration
public double GetAverageLog(TruncatedGaussian that)
Parameters
Type Name Description
TruncatedGaussian that
Returns
Type Description
Double

GetHashCode()

A hash of the distribution parameter values

Declaration
public override int GetHashCode()
Returns
Type Description
Int32
Overrides

GetLogAverageOf(TruncatedGaussian)

Get the logarithm of the average value of that distribution under this distribution, i.e. log(int this(x) that(x) dx)

Declaration
public double GetLogAverageOf(TruncatedGaussian that)
Parameters
Type Name Description
TruncatedGaussian that
Returns
Type Description
Double

GetLogAverageOfPower(TruncatedGaussian, Double)

Get the integral of this distribution times another distribution raised to a power.

Declaration
public double GetLogAverageOfPower(TruncatedGaussian that, double power)
Parameters
Type Name Description
TruncatedGaussian that
Double power
Returns
Type Description
Double

GetLogNormalizer()

Gets the log of the normalizer for the Gaussian density function

Declaration
public double GetLogNormalizer()
Returns
Type Description
Double

GetLogProb(Double)

Get the log probability density at value.

Declaration
public double GetLogProb(double value)
Parameters
Type Name Description
Double value
Returns
Type Description
Double

GetMean()

Returns the mean (first moment) of the distribution

Declaration
public double GetMean()
Returns
Type Description
Double

GetMeanAndVariance(out Double, out Double)

Get the mean and variance after truncation.

Declaration
public void GetMeanAndVariance(out double mean, out double variance)
Parameters
Type Name Description
Double mean
Double variance

GetProbBetween(Double, Double)

Returns the probability mass in an interval.

Declaration
public double GetProbBetween(double lowerBound, double upperBound)
Parameters
Type Name Description
Double lowerBound
Double upperBound
Returns
Type Description
Double

A number between 0 and 1, inclusive.

GetProbLessThan(Double)

Returns the probability of drawing a sample less than x.

Declaration
public double GetProbLessThan(double x)
Parameters
Type Name Description
Double x
Returns
Type Description
Double

A real number in [0,1].

GetQuantile(Double)

Returns the largest value x such that GetProbLessThan(x) <= probability.

Declaration
public double GetQuantile(double probability)
Parameters
Type Name Description
Double probability

A real number in [0,1].
Returns
Type Description
Double

A number

GetVariance()

Get the variance of this distribution

Declaration
public double GetVariance()
Returns
Type Description
Double

IsProper()

Returns true if this distribution is proper

Declaration
public bool IsProper()
Returns
Type Description
Boolean

IsUniform()

Asks whether this instance is uniform. If the upper and lower bounds are finite the distribution is not uniform.

Declaration
public bool IsUniform()
Returns
Type Description
Boolean

True if uniform, false otherwise

MaxDiff(Object)

The maximum difference between the parameters of this distribution and that

Declaration
public double MaxDiff(object thatd)
Parameters
Type Name Description
Object thatd
Returns
Type Description
Double

PointMass(Double)

Create a point mass distribution.

Declaration
[Construction(new string[]{"Point"}, UseWhen = "IsPointMass")]
public static TruncatedGaussian PointMass(double point)
Parameters
Type Name Description
Double point

The location of the point mass
Returns
Type Description
TruncatedGaussian

A new TruncatedGaussian with all probability concentrated on the given point.

Sample()

Sample from the distribution

Declaration
public double Sample()
Returns
Type Description
Double

The sample value

Sample(Double)

Sample from the distribution

Declaration
public double Sample(double result)
Parameters
Type Name Description
Double result

Ignored
Returns
Type Description
Double

The sample value

Sample(Double, Double, Double, Double)

Sample from a TruncatedGaussian distribution with the specified parameters

Declaration
public static double Sample(double mean, double precision, double lowerBound, double upperBound)
Parameters
Type Name Description
Double mean
Double precision
Double lowerBound
Double upperBound
Returns
Type Description
Double

The sample value

SetTo(TruncatedGaussian)

Set this distribution equal to value.

Declaration
public void SetTo(TruncatedGaussian value)
Parameters
Type Name Description
TruncatedGaussian value

SetToPower(TruncatedGaussian, Double)

Set this equal to (dist)^exponent

Declaration
public void SetToPower(TruncatedGaussian dist, double exponent)
Parameters
Type Name Description
TruncatedGaussian dist
Double exponent

SetToProduct(TruncatedGaussian, TruncatedGaussian)

Set this distribution equal to the product of a and b

Declaration
public void SetToProduct(TruncatedGaussian a, TruncatedGaussian b)
Parameters
Type Name Description
TruncatedGaussian a
TruncatedGaussian b

SetToRatio(TruncatedGaussian, TruncatedGaussian, Boolean)

Set this equal to numerator/denominator

Declaration
public void SetToRatio(TruncatedGaussian numerator, TruncatedGaussian denominator, bool forceProper = false)
Parameters
Type Name Description
TruncatedGaussian numerator
TruncatedGaussian denominator
Boolean forceProper

SetToSum(Double, TruncatedGaussian, Double, TruncatedGaussian)

Set the parameters to match the moments of a mixture distribution.

Declaration
public void SetToSum(double weight1, TruncatedGaussian dist1, double weight2, TruncatedGaussian dist2)
Parameters
Type Name Description
Double weight1

The first weight
TruncatedGaussian dist1

The first distribution
Double weight2

The second weight
TruncatedGaussian dist2

The second distribution

SetToUniform()

Set the distribution to uniform with infinite bounds

Declaration
public void SetToUniform()

ToGaussian()

Get the Gaussian with the same moments as this truncated Gaussian.

Declaration
public Gaussian ToGaussian()
Returns
Type Description
Gaussian

ToString()

A human-readable string containing the parameters of the distribution

Declaration
public override string ToString()
Returns
Type Description
String

String representation of the instance
Overrides

Truncate(Double, Double)

Returns the distribution of values restricted to an interval.

Declaration
public ITruncatableDistribution<double> Truncate(double lowerBound, double upperBound)
Parameters
Type Name Description
Double lowerBound
Double upperBound
Returns
Type Description
ITruncatableDistribution<Double>

Uniform()

Construct a uniform truncated Gaussian. This is mathematically equivalent to a uniform Gaussian.

Declaration
[Construction(UseWhen = "IsUniform")]
public static TruncatedGaussian Uniform()
Returns
Type Description
TruncatedGaussian

Operators

Division(TruncatedGaussian, TruncatedGaussian)

Operator overload for division

Declaration
public static TruncatedGaussian operator /(TruncatedGaussian numerator, TruncatedGaussian denominator)
Parameters
Type Name Description
TruncatedGaussian numerator
TruncatedGaussian denominator
Returns
Type Description
TruncatedGaussian

Equality(TruncatedGaussian, TruncatedGaussian)

Equals operator

Declaration
public static bool operator ==(TruncatedGaussian a, TruncatedGaussian b)
Parameters
Type Name Description
TruncatedGaussian a
TruncatedGaussian b
Returns
Type Description
Boolean

ExclusiveOr(TruncatedGaussian, Double)

Operator overload for exponentation

Declaration
public static TruncatedGaussian operator ^(TruncatedGaussian dist, double exponent)
Parameters
Type Name Description
TruncatedGaussian dist
Double exponent
Returns
Type Description
TruncatedGaussian

Inequality(TruncatedGaussian, TruncatedGaussian)

Not equals operator

Declaration
public static bool operator !=(TruncatedGaussian a, TruncatedGaussian b)
Parameters
Type Name Description
TruncatedGaussian a
TruncatedGaussian b
Returns
Type Description
Boolean

Multiply(TruncatedGaussian, TruncatedGaussian)

Operator overload for product.

Declaration
public static TruncatedGaussian operator *(TruncatedGaussian a, TruncatedGaussian b)
Parameters
Type Name Description
TruncatedGaussian a
TruncatedGaussian b
Returns
Type Description
TruncatedGaussian

Implements