discrete

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 Go to latest Published: Apr 3, 2019 License: MIT Imports: 4 Imported by: 11

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Index

Constants

This section is empty.

Variables

This section is empty.

Functions

func CoI 

func CoI(pxyz [][][]float64) float64

func ConditionalEntropy 

func ConditionalEntropy(pxy [][]float64, log lnFunc) float64

ConditionalEntropy calculates the conditional entropy of a probability distribution. It takes the log function as an additional parameter, so that the base can be chosen 

H(X|Y) = -\sum_x p(x,y) lnFunc(p(x,y)/p(y))

func ConditionalEntropyBase2 

func ConditionalEntropyBase2(pxy [][]float64) float64

ConditionalEntropyBase2 calculates the conditional entropy of a probability distribution in bits 

H(X|Y) = -\sum_x p(x,y) log2(p(x,y)/p(y))

func ConditionalEntropyBaseE 

func ConditionalEntropyBaseE(pxy [][]float64) float64

ConditionalEntropyBaseE calculates the conditional entropy of a probability distribution in nats 

H(X|Y) = -\sum_x p(x,y) ln(p(x,y)/p(y))

func ConditionalMutualInformation 

func ConditionalMutualInformation(pxyz [][][]float64, ln lnFunc) float64

ConditionalMutualInformation calculates the conditional mutual information with the given lnFunc function 

I(X,Y|Z) = \sum_x,y, p(x,y,z) (lnFunc(p(x,y|z)) - lnFunc(p(x|z)p(y|z)))

func ConditionalMutualInformationBase2 

func ConditionalMutualInformationBase2(pxyz [][][]float64) float64

ConditionalMutualInformationBase2 calculates the conditional mutual information with base 2 

I(X,Y|Z) = \sum_x,y, p(x,y,z) (log2(p(x,y|z)) - log2(p(x|z)p(y|z)))

func ConditionalMutualInformationBaseE 

func ConditionalMutualInformationBaseE(pxyz [][][]float64) float64

ConditionalMutualInformationBaseE calculates the conditional mutual information with base e I(X,Y|Z) = \sum_x,y, p(x,y,z) (ln(p(x,y|z)) - ln(p(x|z)p(y|z)))

func Create2D 

func Create2D(xDim, yDim int) [][]float64

Create2D creates a 2-dimensional slice

func Create2DInt 

func Create2DInt(xDim, yDim int) [][]int

Create2DInt creates a 2-dimensional slice

func Create3D 

func Create3D(xDim, yDim, zDim int) [][][]float64

Create3D creates a 3-dimensional slice

func Create3DInt 

func Create3DInt(xDim, yDim, zDim int) [][][]int

Create3DInt creates a 3-dimensional slice

func Create4D 

func Create4D(xDim, yDim, zDim, wDim int) [][][][]float64

Create4D creates a 3-dimensional slice

func Empirical1D 

func Empirical1D(d []int) []float64

Empirical1D is an empirical estimator for a one-dimensional probability distribution

func Empirical2D 

func Empirical2D(d [][]int) [][]float64

Empirical2D is an empirical estimator for a two-dimensional probability distribution

func Empirical2DSparse 

func Empirical2DSparse(d [][]int) sm.SparseMatrix

Empirical2DSparse is an empirical estimator for a two-dimensional probability distribution

func Empirical3D 

func Empirical3D(d [][]int) [][][]float64

Empirical3D is an empirical estimator for a three-dimensional probability distribution

func Empirical3DSparse 

func Empirical3DSparse(d [][]int) sm.SparseMatrix

Empirical3DSparse is an empirical estimator for a three-dimensional probability distribution

func Empirical4D 

func Empirical4D(d [][]int) [][][][]float64

Empirical4D is an empirical estimator for a three-dimensional probability distribution

func Entropy 

func Entropy(p []float64, ln lnFunc) float64

Entropy calculates the entropy of a probability distribution. It takes the log function as an additional parameter, so that the base can be chosen: 

H(X) = -\sum_x p(x) lnFunc(p(x))

func EntropyBase2 

func EntropyBase2(p []float64) float64

EntropyBase2 calculates the entropy of a probability distribution with base 2 

H(X) = -\sum_x p(x) log2(p(x))

func EntropyBase2Sparse 

func EntropyBase2Sparse(p sm.SparseMatrix) float64

EntropyBase2Sparse calculates the entropy of a probability distribution with base 2 

H(X) = -\sum_x p(x) log2(p(x))

func EntropyBaseE 

func EntropyBaseE(p []float64) float64

EntropyBaseE calculates the entropy of a probability distribution with base e 

H(X) = -\sum_x p(x) ln(p(x))

func EntropyBaseESparse 

func EntropyBaseESparse(p sm.SparseMatrix) float64

EntropyBaseESparse calculates the entropy of a probability distribution with base e 

H(X) = -\sum_x p(x) ln(p(x))

func EntropyChaoShen 

func EntropyChaoShen(data []int, ln lnFunc) float64

EntropyChaoShen is the Chao-Shen entropy estimator. It take discretised data and the log-function as input Implemented from A. Chao and T.-J. Shen. Nonparametric estimation of shannon’s index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10(4):429–443, 2003.

func EntropyChaoShenBase2 

func EntropyChaoShenBase2(data []int) float64

EntropyChaoShenBase2 is the Chao-Shen entropy estimator. It take discretised data and return bits. Implemented from A. Chao and T.-J. Shen. Nonparametric estimation of shannon’s index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10(4):429–443, 2003.

func EntropyChaoShenBaseE 

func EntropyChaoShenBaseE(data []int) float64

EntropyChaoShenBaseE is the Chao-Shen entropy estimator. It take discretised data and return nats. Implemented from A. Chao and T.-J. Shen. Nonparametric estimation of shannon’s index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10(4):429–443, 2003.

func EntropyHorvitzThompson 

func EntropyHorvitzThompson(data []int, ln lnFunc) float64

EntropyHorvitzThompson is the Horvitz-Thompson entropy estimator. It takes discretised data and log function as input. Implemented from A. Chao and T.-J. Shen. Nonparametric estimation of shannon’s index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10(4):429–443, 2003.

func EntropyHorvitzThompsonBase2 

func EntropyHorvitzThompsonBase2(data []int) float64

EntropyHorvitzThompsonBase2 is the Horvitz-Thompson entropy estimator. It takes discretised data as input and return the entropy in bits. Implemented from A. Chao and T.-J. Shen. Nonparametric estimation of shannon’s index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10(4):429–443, 2003.

func EntropyHorvitzThompsonBaseE 

func EntropyHorvitzThompsonBaseE(data []int) float64

EntropyHorvitzThompsonBaseE is the Horvitz-Thompson entropy estimator. It takes discretised data as input and return the entropy in nats. Implemented from A. Chao and T.-J. Shen. Nonparametric estimation of shannon’s index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10(4):429–443, 2003.

func EntropyMLBC 

func EntropyMLBC(data []int, ln lnFunc) float64

EntropyMLBC is maximum likelihood estimator with bias correction It takes discretised data and the log function as input. Implemented from A. Chao and T.-J. Shen. Nonparametric estimation of shannon’s index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10(4):429–443, 2003.

func EntropyMLBCBase2 

func EntropyMLBCBase2(data []int) float64

EntropyMLBCBase2 is maximum likelihood estimator with bias correction It takes discretised data as input and returns the entropy in bits. Implemented from A. Chao and T.-J. Shen. Nonparametric estimation of shannon’s index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10(4):429–443, 2003.

func EntropyMLBCBaseE 

func EntropyMLBCBaseE(data []int) float64

EntropyMLBCBaseE is maximum likelihood estimator with bias correction It takes discretised data as input and returns the entropy in nats. Implemented from A. Chao and T.-J. Shen. Nonparametric estimation of shannon’s index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10(4):429–443, 2003.

func EntropySparse 

func EntropySparse(p sm.SparseMatrix, ln lnFunc) float64

EntropySparse calculates the entropy of a probability distribution. It takes the log function as an additional parameter, so that the base can be chosen: 

H(X) = -\sum_x p(x) lnFunc(p(x))

func H1 

func H1(px []float64) float64

func H2 

func H2(pxy [][]float64) float64

func H3 

func H3(pxyz [][][]float64) float64

func InformationDecomposition 

func InformationDecomposition(pxyz [][][]float64, resolution int) (float64, float64, float64)

InformationDecomposition return the UI(X;Y\Z), UI(X;Z\Y), CI(X;Y,Z), and SI(X;Y,Z) according to N. Bertschinger, J. Rauh, E. Olbrich, J. Jost, and N. Ay, Quantifying unique information, CoRR, 2013

func MiXvY 

func MiXvY(pxyz [][][]float64) float64

func MiXvYZ 

func MiXvYZ(pxyz [][][]float64) float64

func MiXvYgZ 

func MiXvYgZ(pxyz [][][]float64) float64

func MiXvZgY 

func MiXvZgY(pxyz [][][]float64) float64

func MinMax 

func MinMax(pxyz [][][]float64, resolution int) (float64, float64, float64, float64, float64, float64)

func MutualInformation 

func MutualInformation(pxy [][]float64, log lnFunc) float64

MutualInformation calculates the mutual information with the given lnFunc function 

I(X,Y) = \sum_x,y p(x,y) (lnFunc(p(x,y)) - lnFunc(p(x)p(y)))

func MutualInformationBase2 

func MutualInformationBase2(pxy [][]float64) float64

MutualInformationBase2 calculates the mutual information with base 2 

I(X,Y) = \sum_x,y p(x,y) (log2(p(x,y)) - log2(p(x)p(y)))

func MutualInformationBaseE 

func MutualInformationBaseE(pxy [][]float64) float64

MutualInformationBaseE calculates the mutual information with base e 

I(X,Y) = \sum_x,y p(x,y) (ln(p(x,y)) - ln(p(x)p(y)))

func Normalise1D 

func Normalise1D(a []float64) []float64

Normalise1D return the normalised matrix 

a / sum(a)

func Normalise2D 

func Normalise2D(a [][]float64) [][]float64

Normalise2D return the normalised matrix 

a / sum(a)

func Normalise3D 

func Normalise3D(a [][][]float64) [][][]float64

Normalise3D return the normalised matrix 

a / sum(a)

func Normalise4D 

func Normalise4D(a [][][][]float64) [][][][]float64

Normalise4D return the normalised matrix 

a / sum(a)

func PX 

func PX(pxyz [][][]float64) []float64

func PXY 

func PXY(pxyz [][][]float64) [][]float64

func PXZ 

func PXZ(pxyz [][][]float64) [][]float64

func PY 

func PY(pxyz [][][]float64) []float64

func PYZ 

func PYZ(pxyz [][][]float64) [][]float64

func PZ 

func PZ(pxyz [][][]float64) []float64

func Pt 

func Pt(pxyz [][][]float64, a, b float64) [][][]float64

Types

type IterativeScaling 

type IterativeScaling struct {
	PTarget             []float64
	PEstimate           []float64
	Features            map[string][]int
	NrOfIterations      int
	ErrorThreshold      float64
	Alphabet            [][]int
	NrOfStates          []int
	NrOfVariables       int
	CurrentFeatureIndex int
	CurrentIteration    int
	LastKLStep          float64
	Keys                []string
}

IterativeScaling contains the configuration and data required for the iterative scaling algorithm

func NewIterativeScaling 

func NewIterativeScaling() *IterativeScaling

NewIterativeScaling Creates a new struct

func (*IterativeScaling) CalculateMarginalProbability 

func (data *IterativeScaling) CalculateMarginalProbability(feature []int) float64

CalculateMarginalProbability calculates the marginal probability p(x)

func (*IterativeScaling) CreateAlphabet 

func (data *IterativeScaling) CreateAlphabet()

CreateAlphabet creates the alphabet given NrOfStates and NrOfVariables

func (*IterativeScaling) Init 

func (data *IterativeScaling) Init()

Init extract the feature names for faster processing

func (*IterativeScaling) Iterate 

func (data *IterativeScaling) Iterate()

Iterate implements the iterative scaling algorithm as described in I. Csiszar. i-divergence geometry of probability distributions and minimization problems. Ann. Probab., 3(1):146–158, 02 1975. Input is a probability distribution, a feature set, and a number of iterations. The output is the maximum entropy estimation of p given the feature set p_est^(n+1)(x) = p_target(x_a) * p_est^(n)(x_{without a}|x_a) where a is cycled through the list of features We calculate it in the following form: p_est^(n+1)(x) = p_est^(n)(x) * p_target(x_a) / p_est(x_a)

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