Package 'MoTBFs'

Description

Takes a "jointmotbf" object and contructs an R function to evaluate it at multidimensional points.

Usage

## S3 method for class 'jointmotbf'
as.function(x, ...)

Arguments

Details

This is an S3 method for the generic function as.function.

Value

It returns a function to evaluate an object of class "jointmotbf".

See Also

parametersJointMoTBF and jointMoTBF

Examples

## 1.EXAMPLE
## Dataset
data <- data.frame(X = rnorm(100), Y = rexp(100))

## Joint function
dim <- c(3,2)
param <- parametersJointMoTBF(data, dimensions = dim)
P <- jointMoTBF(param)
density <- as.function(P)(data[,1], data[,2])
density

## Log-likelihood
sum(log(density))

#############################################################################
## MORE EXAMPLES ############################################################
#############################################################################

## Dataset
data <- data.frame(X = rnorm(100), Y = rexp(100), Z = rnorm(100))

## Joint function
dim <- c(2,3,4)
param <- parametersJointMoTBF(data, dimensions = dim)
P <- jointMoTBF(param)
density <- as.function(P)(data[,1], data[,2], data[,3])
density

## Log-likelihood
sum(log(density))

Description

Takes an "motbf" object and contructs an R function to evaluate it at points.

Usage

## S3 method for class 'motbf'
as.function(x, ...)

Arguments

Details

This is an S3 method for the generic function as.function.

Value

It returns a function to evaluate an object of class "motbf".

Examples

## Data
X <- rchisq(5000, df = 3)

## Learning
P <- univMoTBF(X, POTENTIAL_TYPE = "MOP"); P

## Evaluation
as.function(P)(min(X))
as.function(P)(max(X))
as.function(P)(10)
density <- as.function(P)(X)

## Plot
hist(X, prob = TRUE, main = "")
points(X, density, col=4, pch=16)

Description

This function builds a string with the structure of a 'mop' function.

Usage

asMOPString(parameters)

Arguments

Value

A "character" string with a 'mop' structure.

Examples

param <- c(1,2,3,4)
asMOPString(param)

param <- 3.4
asMOPString(param)

Description

This function builds a string with the structure of an 'mte' function.

Usage

asMTEString(parameters, num = 5)

Arguments

Value

A "character" string with an 'mte' structure.

Examples

param <- -5.8
asMTEString(param)

param <- c(5.2,0.3,-3,4)
asMTEString(param)

Description

Computes the Bayesian information criterion value (BIC) of a mixture of truncated basis functions. The BIC score is the log likelihood penalized by the number of parameters of the function and the number of records of the evaluated data.

Usage

BICMoTBF(Px, X)

Arguments

Value

A "numeric" value corresponding to the BIC score.

See Also

univMoTBF

Examples

## Data
X <- rexp(10000)

## Data test
Xtest <- rexp(1000)
Xtest <- Xtest[Xtest>=min(X) & Xtest<=max(X)]

## Learning
f1 <- univMoTBF(X, POTENTIAL_TYPE = "MOP", nparam = 10); f1
f2 <- univMoTBF(X, POTENTIAL_TYPE = "MTE", maxParam = 11); f2

## BIC values
BICMoTBF(Px = f1, X = Xtest)
BICMoTBF(Px = f2, X = Xtest)

Description

Compute the BIC score using more than one probability functions.

Usage

BICMultiFunctions(Px, X)

Arguments

Value

The "numeric" BIC value.

See Also

univMoTBF

Examples

## Data
X <- rnorm(500)
Y <- rnorm(500, mean=1)
data <- data.frame(X=X, Y=Y)
## Data as a "list"
Xlist <- sapply(data, list)

## Learning as a "list"
Plist <- lapply(data, univMoTBF, POTENTIAL_TYPE="MOP")
Plist

## BIC value
BICMultiFunctions(Px=Plist, X=Xlist)

Description

Defines an object of class "jointmotbf" and other basic functions for manipulating "jointmotbf" objects.

Usage

jointmotbf(x = 0)

## S3 method for class 'jointmotbf'
print(x, ...)

## S3 method for class 'jointmotbf'
as.character(x, ...)

## S3 method for class 'jointmotbf'
as.list(x, ...)

is.jointmotbf(x, class = "jointmotbf")

Arguments

See Also

jointMoTBF

Examples

## n.parameters is the product of the dimensions
dim <- c(3,3)
param <- seq(1,prod(dim), by=1)
## Joint Function 
f <- list(Parameters=param, Dimensions=dim)
jointF <- jointMoTBF(f)

print(jointF) ## jointF
as.character(jointF)
as.list(jointF)
is(jointF)
is.jointmotbf(jointF)

Description

Defines an object of class "motbf" and other basic functions for manipulating "motbf" objects.

Usage

motbf(x = 0)

## S3 method for class 'motbf'
print(x, ...)

## S3 method for class 'motbf'
as.character(x, ...)

## S3 method for class 'motbf'
as.list(x, ...)

is.motbf(x, class = "motbf")

Arguments

See Also

asMOPString and asMTEString

Examples

## Subclass 'MOP'
param <- c(1,2,3,4,5)
MOPString <- asMOPString(param)
fMOP <- motbf(MOPString)
print(fMOP) ## fMOP
as.character(fMOP)
as.list(fMOP)
is(fMOP) 
is.motbf(fMOP)

## Subclass 'MTE'
param <- c(6,7,8,9,10)
MTEString <- asMTEString(param)
fMTE <- motbf(MTEString)
print(fMTE) ## MTE
as.character(fMTE)
as.list(fMTE)
is(fMTE) 
is.motbf(fMTE)

Description

Clean the memory. Delete all the objects in memory and a garbage collection takes place.

Usage

clean(envir = globalenv(), n = 2)

Arguments

Examples

## Run to clean the environment
clean()
clean(n=2)

Description

Extracts the parameters of a joint MoTBF density.

Usage

## S3 method for class 'jointmotbf'
coef(object, ...)

Arguments

Value

A "numeric" vector with the parameters of the function.

See Also

parametersJointMoTBF and jointMoTBF

Examples

## Generate a dataset
data <- data.frame(X1 = rnorm(100), X2 = rnorm(100))

## Joint function
dim <-c(2,4)
param <- parametersJointMoTBF(data, dimensions = dim)
P <- jointMoTBF(param)
P$Time

## Coefficients
coef(P)

#############################################################################
## MORE EXAMPLES ############################################################
#############################################################################

## Generate a dataset
data <- data.frame(X1 = rnorm(100), X2 = rnorm(100), X3 = rnorm(100))
 
## Joint function
dim <-c(2,4,3)
param <- parametersJointMoTBF(data, dimensions = dim)
P <- jointMoTBF(param)
P$Time

## Coefficients
coef(P)

Description

It extracts the parameters of the learned mixtures of polynomial models.

Usage

coeffMOP(fx)

coeffPol(fx)

Arguments

Details

coeffMOP() return the coefficients of the terms in the function.

coeffPol() returns the coefficients of the potential of the polynomial basis in the function.

Value

An array with the parameters of the function.

See Also

coef.motbf and univMoTBF

Examples

## 1. EXAMPLE
data <- rchisq(1000, df=5)
fx1 <- univMoTBF(data, POTENTIAL_TYPE = "MOP")
hist(data, prob=TRUE, main="")
plot(fx1, xlim=range(data), col="red", add=TRUE)
coeffMOP(fx1) ## coef(fx1)
coeffPol(fx1)

## 2. EXAMPLE
data <- rexp(1000, rate=1/2)
fx2 <- univMoTBF(data, POTENTIAL_TYPE = "MOP")
hist(data, prob=TRUE, main="")
plot(fx2, xlim=range(data), col="red", add=TRUE)
coeffMOP(fx2) ## coef(fx2)
coeffPol(fx2)

Description

Extracts the parameters of the learned mixtures of truncated basis functions.

Usage

## S3 method for class 'motbf'
coef(object, ...)

Arguments

Value

A numeric vector with the parameters of the function.

See Also

univMoTBF, coeffMOP and coeffMTE

Examples

## Data
X <- rchisq(2000, df = 5)

## Learning
f1 <- univMoTBF(X, POTENTIAL_TYPE = "MOP"); f1
## Coefficients
coef(f1)

## Learning
f2 <- univMoTBF(X, POTENTIAL_TYPE = "MTE", maxParam = 10); f2
## Coefficients
coef(f2)

## Learning
f3 <- univMoTBF(X, POTENTIAL_TYPE = "MOP", nparam=10); f3
## Coefficients
coef(f3)

## Plots
plot(NULL, xlim = range(X), ylim = c(0,0.2), xlab="X", ylab="density")
plot(f1, xlim = range(X), col = 1, add = TRUE)
plot(f2, xlim = range(X), col = 2, add = TRUE)
plot(f3, xlim = range(X), col = 3, add = TRUE)
hist(X, prob = TRUE, add= TRUE)

Description

It extracts the parameters of the learned mixtures of truncated exponential models.

Usage

coeffMTE(fx)

coeffExp(fx)

Arguments

Details

coeffMOP() return the coefficients of the terms in the function.

coeffPol() returns the coefficients of the potential of the exponential basis in the function.

Value

An array with the parameters of the function.

See Also

coef.motbf and univMoTBF

Examples

## 1. EXAMPLE
data <- rnorm(1000, mean=5)
fx1 <- univMoTBF(data, POTENTIAL_TYPE = "MTE")
hist(data, prob=TRUE, main="")
plot(fx1, xlim=range(data), col="red", add=TRUE)
coeffMTE(fx1) ## coef(fx1)
coeffExp(fx1)

## 2. EXAMPLE
data <- rexp(1000, rate=1/2)
fx2 <- univMoTBF(data, POTENTIAL_TYPE = "MTE")
hist(data, prob=TRUE, main="")
plot(fx2, xlim=range(data), col="red", add=TRUE)
coeffMTE(fx2) ## coef(fx2)
coeffExp(fx2)

Description

Compute the degree for each term of a joint CDF.

Usage

coefExpJointCDF(dimensions)

Arguments

Value

A list with n element. Each element contains a numeric vector with the degree for each variable and each term of the joint CDF.

Examples

## Dimension of the joint PDF of 2 variables
dim <- c(4,5) 
## Potentials of each term of the CDF
c <- coefExpJointCDF(dim)
length(c) + 1 ## plus 1 because of the constant coefficient

## Dimension of the joint density function of 2 variables
dim <- c(5,5,3)
## Potentials of the cumulative function
coefExpJointCDF(dim)

Description

Collection of functions used for learning conditional MoTBFs, computing the internal BIC, selecting the parents that get the best BIC value, and other internal functions required to learn the conditional densities.

Usage

conditionalMethod(
  data,
  nameParents,
  nameChild,
  numIntervals,
  POTENTIAL_TYPE,
  maxParam = NULL,
  s = NULL,
  priorData = NULL
)

conditional(
  data,
  nameParents,
  nameChild,
  domainChild,
  domainParents,
  numIntervals,
  mm,
  POTENTIAL_TYPE,
  maxParam = NULL,
  s = NULL,
  priorData = NULL
)

select(
  data,
  nameParents,
  nameChild,
  domainChild,
  domainParents,
  numIntervals,
  POTENTIAL_TYPE,
  maxParam = NULL,
  s = NULL,
  priorData = NULL
)

learn.tree.Intervals(
  data,
  nameParents,
  nameChild,
  domainParents,
  domainChild,
  numIntervals,
  POTENTIAL_TYPE,
  maxParam = NULL,
  s = NULL,
  priorData = NULL
)

BICscoreMoTBF(conditionalfunction, data, nameParents, nameChild)

Arguments

Details

The main function, conditionalMethod(), fits truncated basis functions for the conditioned variable for each configuration of splits of the parent variables. The domain of the parent variables is splitted in different intervals and univariate functions are fitted in these ranges. The remaining above described functions are internal to the main function.

Value

The main function conditionalMethod returns a list with the name of the parents, the different intervals and the fitted densities

See Also

printConditional

Examples

## Dataset
X <- rnorm(1000)
Y <- rbeta(1000, shape1 = abs(X)/2, shape2 = abs(X)/2)
Z <- rnorm(1000, mean = Y)
data <- data.frame(X = X, Y = Y, Z = Z)

## Conditional Method
parents <- c("X","Y")
child <- "Z"
intervals <- 2

potential <- "MTE"
fMTE <- conditionalMethod(data, nameParents = parents, nameChild = child, 
numIntervals = intervals, POTENTIAL_TYPE = potential)
printConditional(fMTE)

##############################################################################

potential <- "MOP"
fMOP <- conditionalMethod(data, nameParents = parents, nameChild = child,
numIntervals = intervals, POTENTIAL_TYPE = potential, maxParam = 15)
printConditional(fMOP)

##############################################################################

##############################################################################
## Internal functions: Not needed to run #####################################
##############################################################################

domainP <- range(data[,parents])
domainC <- range(data[, child])
t <- conditional(data, nameParents = parents, nameChild = child,
domainParents = domainP, domainChild = domainC, numIntervals = intervals,
mm = NULL, POTENTIAL_TYPE = potential)
printConditional(t)
selection <- select(data, nameParents = parents, nameChild = child,
domainParents = domainP, domainChild = domainC, numIntervals = intervals,
POTENTIAL_TYPE = potential)
parent1 <- selection$parent; parent1
domainParent1 <- range(data[,parent1])
treeParent1 <- learn.tree.Intervals(data, nameParents = parent1,
nameChild = child, domainParents = domainParent1, domainChild = domainC,
numIntervals = intervals, POTENTIAL_TYPE = potential)
BICscoreMoTBF(treeParent1, data, nameParents = parent1, nameChild = child)

###############################################################################
###############################################################################

Description

Collection of functions for discretizing, standardizing, converting factors to characters and other usufull methods for pre-processing datasets.

Usage

whichDiscrete(dataset, discreteVariables)

discreteVariables_as.character(dataset, discreteVariables)

standardizeDataset(dataset)

discretizeVariablesEWdis(dataset, numIntervals, factor = FALSE, binary = FALSE)

discreteVariablesStates(namevariables, discreteData)

nstates(DiscreteVariablesStates)

quantileIntervals(X, numIntervals)

scaleData(dataset, scale)

Arguments

Details

whichDiscrete() selects the position of the discrete variables.

discreteVariables_as.character() transforms the values of the discrete variables into character values.

standardizeDataset() standardizes all the variables in a data set.

discretizeVariablesEWdis() discretizes the continuous variables in a dataset using equal width binning.

discreteVariablesStates() extracts the states of the qualitative variables.

nstates() computes the number of different values of the discrete variables.

quantileIntervals() gets the quantiles of a variable taking into account the number of intervals into which its domain is splitted.

Examples

## dataset: 2 continuous variables, 1 discrete variable.
data <- data.frame(X = rnorm(100),Y = rexp(100,1/2), Z = as.factor(rep(c("s","a"), 50)))
disVar <- "Z" ## Discrete variable
class(data[,disVar]) ## factor

data <- discreteVariables_as.character(dataset = data, discreteVariables = disVar)
class(data[,disVar]) ## character

whichDiscrete(dataset = data, discreteVariables = "Z")

standData <- standardizeDataset(dataset = data)

disData <- discretizeVariablesEWdis(dataset = data, numIntervals = 3)

l <- discreteVariablesStates(namevariables = names(data), discreteData = disData)

nstates(DiscreteVariablesStates = l)

## Continuous variables
quantileIntervals(X = data[,1], numIntervals = 4)
quantileIntervals(X = data[,2], numIntervals = 10)

Description

Compute the derivative of an "motbf" object with 'mop' subclass.

Usage

derivMOP(fx)

Arguments

Value

The derivative which is also an "motbf" function.

See Also

univMoTBF for learning and derivMoTBF for general "motbf" models.

Examples

## 1. EXAMPLE
X <- rexp(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MOP")
derivMOP(Px)

## 2. EXAMPLE
X <- rnorm(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MOP")
derivMOP(Px)

## Not run: 
## 3. EXAMPLE
X <- rnorm(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MTE")
derivMOP(Px)
## Error in derivMOP(Px): fx is an 'motbf' function but not 'mop' subclass.
class(Px)
subclass(Px)

## End(Not run)

Description

Compute the derivative of a one-dimensional mixture of truncated basis function.

Usage

derivMoTBF(fx)

Arguments

Value

The derivative of the MoTBF function, which is also an object of class "motbf".

See Also

univMoTBF, derivMOP and derivMTE

Examples

## 1. EXAMPLE
X <- rexp(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MOP")
derivMoTBF(Px)

## 2. EXAMPLE
X <- rnorm(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MOP")
derivMoTBF(Px)

## 3. EXAMPLE
X <- rchisq(1000, df = 3)
Px <- univMoTBF(X, POTENTIAL_TYPE="MTE")
derivMoTBF(Px)

## Not run: 
## 4. EXAMPLE
Px <- "x+2"
class(Px)
derivMoTBF(Px)
## Error in derivMoTBF(Px): "fx is not an 'motbf' function."

## End(Not run)

Description

Compute the derivative of an "motbf" object with 'mte' subclass.

Usage

derivMTE(fx)

Arguments

Value

The derivative which is also an "motbf" function.

See Also

univMoTBF for learning and derivMoTBF for general "motbf" models.

Examples

## 1. EXAMPLE
X <- rexp(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MTE")
derivMTE(Px)

## 2. EXAMPLE
X <- rnorm(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MTE")
derivMTE(Px)

## Not run: 
## 3. EXAMPLE
X <- rnorm(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MOP")
derivMTE(Px)
## Error in derivMTE(Px): fx is an 'motbf' function but not 'mte' subclass.
class(Px)
subclass(Px)

## End(Not run)

Description

Get the dimension of "motbf" and "jointmotbf" densities.

Usage

dimensionFunction(P)

Arguments

Value

Dimension of the function.

See Also

univMoTBF and jointMoTBF

Examples

## 1. EXAMPLE 
## Data
X <- rnorm(2000)

## Univariate function
subclass <- "MOP"
f <- univMoTBF(X, POTENTIAL_TYPE = subclass)
dimensionFunction(f)

## 2. EXAMPLE 
## Dataset with 2 variables
X <- data.frame(rnorm(100), rnorm(100))

## Joint function
dim <- c(2,3)
param <- parametersJointMoTBF(X, dimensions = dim)
P <- jointMoTBF(param)

## Dimension of the joint function
dimensionFunction(P)

Description

This function returns the states of all discrete nodes from a list obtained from MoTBFs_Learning.

Usage

discreteStatesFromBN(bn, dag)

Arguments

Value

discreteStatesFromBN returns a list of length equal to the number of discrete nodes in the network. Each element of the list corresponds to a node and contains a character vector indicating the states of the node.

Examples

## Create a dataset
  # Continuous variables
  x <- rnorm(100)
  y <- rnorm(100)
  
  # Discrete variable
  z <- sample(letters[1:2],size = 100, replace = TRUE)
  
  data <- data.frame(C1 = x, C2 = y, D1 = z, stringsAsFactors = FALSE)
  
## Get DAG
  dag <- LearningHC(data)

## Learn a BN
  bn <- MoTBFs_Learning(dag, data, POTENTIAL_TYPE = "MTE")

## Get the states of the discrete nodes

  discreteStatesFromBN(bn, dag)

Description

This data set contains information of Escherichia coli. It is a bacterium of the genus Escherichia that is commonly found in the lower intestine of warm-blooded organism.

Format

A data frame with 336 rows, 8 variables and the class.

Details

Sequence Name

Accession number for the SWISS-PROT database.

mcg

McGeoch's method for signal sequence recognition.

gvh

Von Heijne's method for signal sequence recognition.

lip

Von Heijne's Signal Peptidase II consensus sequence score. Binary attribute.

chg

Presence of charge on N-terminus of predicted lipoproteins. Binary attribute.

aac

Score of discriminant analysis of the amino acid content of outer membrane and periplasmic proteins.

alm1

Score of the ALOM membrane spanning region prediction program.

alm2

Score of ALOM program after excluding putative cleavable signal regions from the sequence.

Class

Class variable. 8 possibles states.

Source

http://archive.ics.uci.edu/ml/datasets/Ecoli

Description

Evaluates a "jointmotbf" object at a specific point.

Usage

evalJointFunction(P, values)

Arguments

Value

If all the variables in the equation are evaluated then a "numeric" value is returned. Otherwise, an "motbf" object or a "jointmotbf" object is returned.

Examples

#' ## 1. EXAMPLE
## Dataset with 2 variables
X <- data.frame(rnorm(100), rexp(100))

## Joint function
dim <- c(3,3) # dim <- c(5,4)
param <- parametersJointMoTBF(X, dimensions = dim)
P <- jointMoTBF(param)
P

## Evaluation
nVariables(P)
val <- list(x = -1.5, y = 3)
evalJointFunction(P, values = val)
val <- list(x = -1.5)
evalJointFunction(P, values = val)
val <- list(y = 3)
evalJointFunction(P, values = val)

##############################################################################
## MORE EXAMPLES #############################################################
############################################################################## 

## Dataset with 3 variables
X <- data.frame(rnorm(100), rexp(100), rnorm(100, 1))

## Joint function
dim <- c(2,1,3)
param <- parametersJointMoTBF(X, dimensions = dim)
P <- jointMoTBF(param)
P

## Evaluation
nVariables(P)
val <- list(x = 0.8, y = -2.1, z = 1.2)
evalJointFunction(P, values = val)
val <- list(x = 0.8, z = 1.2)
evalJointFunction(P, values = val)
val <- list(y = -2.1)
evalJointFunction(P, values = val)
val <- list(y = -2.1)
evalJointFunction(P, values = val)

Description

This function returns the conditional probability function of a node given an MoTBF-bayesian network and the value of its parents.

Usage

findConditional(node, bn, evi = NULL)

Arguments

Value

A list containing the conditional distribution of the target variable.

Examples

## Dataset
  data("ecoli", package = "MoTBFs")
  data <- ecoli[,-c(1,9)]

## Get directed acyclic graph
  dag <- LearningHC(data)
  
## Learn bayesian network
  bn <- MoTBFs_Learning(dag, data = data, numIntervals = 4, POTENTIAL_TYPE = "MTE")
  
## Specify the evidence set and node of interest
  evi <- data.frame(lip = "0.48", alm1 = 0.55, gvh = 1, stringsAsFactors=FALSE)
  node = "alm2"
  
## Get the conditional distribution
  findConditional(node, bn, evi)

Description

forward_sampling() returns the conditional distribution of a target variable given a set of oberved variables. The forward sampling algorithm approximates the conditional distribution from a random sample.

Usage

forward_sampling(bn, dag, target, evi, size, ...)

Arguments

Value

A list containing the conditional distribution of the target variable and a data.frame with the generated sample.

References

Henrion, M. (1988). Propagating uncertainty in Bayesian networks by probabilistic logic sampling. In Machine Intelligence and Pattern Recognition (Vol. 5, pp. 149-163). North-Holland.

Examples

## Dataset
  data("ecoli", package = "MoTBFs")
  data <- ecoli[,-c(1,9)]

## Get directed acyclic graph
  dag <- LearningHC(data)
  
## Learn bayesian network
  bn <- MoTBFs_Learning(dag, data = data, numIntervals = 4, POTENTIAL_TYPE = "MTE")
  
## Specify the evidence set and target variable
  obs <- data.frame(lip = "0.48", alm1 = 0.55, gvh = 1, stringsAsFactors=FALSE)
  node <- "alm2"
  
## Get the conditional distribution of 'node' and the generated sample
  forward_sampling(bn, dag, target = node, evi = obs, size = 10, maxParam = 15)

Description

Generate a prior dataset taking in to account the relationships between the varibles in a given network.

Usage

generateNormalPriorData(graph, data, size, means, deviations = NULL)

Arguments

Value

A normal prior data set of class "data.frame".

See Also

rnormMultiv

Examples

## Data
data(ecoli)
data <- ecoli[,-c(1,9)] ## remove sequece.name and class
X <- TrainingandTestData(data, percentage_test = 0.95)
Xtraining <- X$Training
Xtest <- X$Test

## DAG
dag <- LearningHC(data)
plot(dag)

## Means and desviations
colnames(data)

m <- sapply(data, function(x){ifelse(is.numeric(x), mean(x),NA)})
d <- sapply(data, function(x){ifelse(is.numeric(x), sd(x),NA)})


## Prior Dataset
n <- 5600
priorData <- generateNormalPriorData(dag, data = Xtraining, size = n, means = m)
summary(priorData)
ncol(priorData)
nrow(priorData)
class(priorData)

Description

Compute the parents of each variable in the graph.

Usage

getChildParentsFromGraph(graph, nameVars = NULL)

Arguments

Value

A list where each element is a vector containing the name of a variable and its parents in the graph.

Examples

## Data
data(ecoli)
ecoli <- ecoli[,-1] ## Sequence Name

## DAG1
dag1 <- LearningHC(ecoli)
dag1
plot(dag1)
getChildParentsFromGraph(dag1)

## DAG2
dag2 <- LearningHC(ecoli, numIntervals = 10)
dag2
plot(dag2)
getChildParentsFromGraph(dag2)

Description

Compute the coefficients for the linear opinion pool

Usage

getCoefficients(fPI, rangeNewPriorData, fD, data, domain, coeffversion)

Arguments

Details

coeffversion can be: "1" coef1 and coef2 are the sum of the probabilities of one of the function over the sum of all probabilities, respectively; "2" coef1 and coef2 are the solution of a linear optimization problem which tries to maximize the sum 1 for each row of probabilities; "3" coef1 and coef2 are the difference of the log-likelihood of the evaluated model and a random uniform model over the sum of both differences, respectively; "4" coef1 and coef2 are the difference of the log-likelihood of the evaluated model and a ramdom positive MoTBF model over the sum of both differences, respectively.

Value

A "numeric" value of length 2 giving the coefficients which are the weigth of the two function to combine.

See Also

learnMoTBFpriorInformation

Examples

## Data
X <- rnorm(15)

## Prior Data
priordata <- rnorm(5000)

## Learning
confident <- 5
type <- "MOP"
f <- learnMoTBFpriorInformation(priorData = priordata, data = X, s = confident,
POTENTIAL_TYPE = type)
attributes(f)
 
## Coefficients: linear opinion pool
getCoefficients(fPI = f$priorFunction, rangeNewPriorData = f$domain, fD = f$dataFunction, 
data = X, domain = range(X), coeffversion = 4)

getCoefficients(fPI = f$priorFunction, rangeNewPriorData = f$domain, fD = f$dataFunction, 
data = X, domain = range(X), coeffversion = 1)

getCoefficients(fPI = f$priorFunction, rangeNewPriorData = f$domain, fD = f$dataFunction, 
data = X, domain = range(X), coeffversion = 3)

getCoefficients(fPI = f$priorFunction, rangeNewPriorData = f$domain, fD = f$dataFunction, 
data = X, domain = range(X), coeffversion = 2)

Description

Generates a non normalized (i.e. not integrating to 1) positive MoTBF function.

Usage

getNonNormalisedRandomMoTBF(degree, POTENTIAL_TYPE = "MOP")

Arguments

Value

A "numeric" vector of length 2 giving the coefficients.

Examples

getNonNormalisedRandomMoTBF(8, POTENTIAL_TYPE = "MOP")
getNonNormalisedRandomMoTBF(11, POTENTIAL_TYPE = "MTE")

Description

Compute the loglikelihood and the BIC score for discrete models, i.e multinomial Bayesian Networks.

Usage

getlogLikelihoodDiscreteBN(discreteBN)

getBICDiscreteBN(discreteBN, sameData = FALSE)

Arguments

Value

The loglikelihood and the BIC score of the discrete network.

Examples

## 1. EXAMPLE 
## Discrete data
X <- rep(c("yes", "no", "maybe"), 500)
Y <- rep(c("M", "F"), 750)
data <- data.frame(X=X, Y=Y)
disVar <- c("X","Y")
data <- discreteVariables_as.character(data, discreteVariables=disVar)
n <- nrow(data)

## Probabilities
s <- discreteVariablesStates(namevariables=disVar, discreteData=data)
p <- lapply(1:length(s), function(i) probDiscreteVariable(stateNames=
s[[i]]$states, Variable=data[,i]))

## Log-likelihood
getlogLikelihoodDiscreteBN(p)

## BIC
getBICDiscreteBN(p, sameData = TRUE)

## 2. EXAMPLE 
## Discrete variables
X <- rep(c("1", "2", "3"), 500)
data <- data.frame(X=as.character(X))
s <- discreteVariablesStates(namevariables="X", discreteData=data)
p1 <- probDiscreteVariable(stateNames = s[[1]]$states, Variable = data[,1])

Y <- rep(c("YES", "NO"), 100)
data <- data.frame(Y = as.character(Y))
s <- discreteVariablesStates(namevariables = "Y", discreteData = data)
p2 <- probDiscreteVariable(stateNames = s[[1]]$states, Variable = data[,1])
## Probabilities
P <- list(p1,p2)

## Log-likelihood
getlogLikelihoodDiscreteBN(P)

## BIC
getBICDiscreteBN(P, sameData = TRUE)

Description

Compute the BIC score and the loglikelihood from the fitted MoTBFs functions in a hybrid Bayesian network.

Usage

logLikelihood.MoTBFBN(MoTBF.BN, data)

BiC.MoTBFBN(MoTBF.BN, data)

Arguments

Value

A numeric value giving the log-likelihood of the BN.

See Also

MoTBFs_Learning

Examples

## Dataset Ecoli
require(MoTBFs)
data(ecoli)
data <- ecoli[,-c(1)] ## remove variable sequence

## Directed acyclic graph
dag <- LearningHC(data)

## Learning BN
intervals <- 3
potential <- "MOP"
P1 <- MoTBFs_Learning(graph = dag, data = data, POTENTIAL_TYPE=potential,
numIntervals = intervals, maxParam = 5)
logLikelihood.MoTBFBN(P1, data) ##BIC$LogLikelihood
BIC <- BiC.MoTBFBN(P1, data)
BIC$BIC

## Learning BN
intervals <- 2
potential <- "MTE"
P2 <- MoTBFs_Learning(graph = dag, data = data, POTENTIAL_TYPE=potential,
numIntervals = intervals, maxParam = 10)
logLikelihood.MoTBFBN(P2, data) ##BIC$LogLikelihood
BIC <- BiC.MoTBFBN(P2, data)
BIC$BIC

Description

Integrate a "jointmotbf" object over an non defined domain. It is able to get the integral of a joint function over a set of variables or over all the variables in the function.

Usage

integralJointMoTBF(P, var = NULL)

Arguments

Value

A multiintegral of a joint function of class "jointmotbf".

Examples

## 1. EXAMPLE
## Dataset with 2 variables
X <- data.frame(rnorm(100), rnorm(100))

## Joint function
dim <- c(2,3)
param <- parametersJointMoTBF(X, dimensions = dim)
P <- jointMoTBF(param)

## Integral
integralJointMoTBF(P)
integralJointMoTBF(P, var="x")
integralJointMoTBF(P, var="y")

##############################################################################
## MORE EXAMPLES #############################################################
##############################################################################

## Dataset with 3 variables
X <- data.frame(rnorm(50), rnorm(50), rnorm(50))

## Joint function
dim <- c(2,1,3)
param <- parametersJointMoTBF(X, dimensions = dim)
P <- jointMoTBF(param)
 
## Integral
integralJointMoTBF(P)
integralJointMoTBF(P, var="x")
integralJointMoTBF(P, var="y")
integralJointMoTBF(P, var="z")
integralJointMoTBF(P, var=c("x","z"))

Description

Method to calculate the non-defined integral of an "motbf" object of 'mte' subclass.

Usage

integralMOP(fx)

Arguments

Value

The non-defined integral of the function.

See Also

univMoTBF for learning and integralMoTBF for a more complete function to get defined and non-defined integrals of class "motbf".

Examples

## 1. EXAMPLE
X <- rexp(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MOP")
integralMOP(Px)

## 2. EXAMPLE
X <- rnorm(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MOP")
integralMOP(Px)

## Not run: 
## 3. EXAMPLE
X <- rnorm(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MTE")
integralMOP(Px)
## Error in integralMOP(Px): fx is an 'motbf' function but not 'mop' subclass.
class(Px)
subclass(Px)

## End(Not run)

Description

Compute the integral of a one-dimensional mixture of truncated basis function over a bounded or unbounded interval.

Usage

integralMoTBF(fx, min = NULL, max = NULL)

Arguments

Details

If the limits of the interval, min and max are NULL, then the output is the expression of the indefinite integral. If only 'min' contains a numeric value, then the expression of the integral is evaluated at this point.

Value

integralMoTBF() returns either the indefinite integral of the MoTBF function, which is also an object of class "motbf", or the definite integral, wich is a "numeric" value.

See Also

univMoTBF, integralMOP and integralMTE

Examples

## 1. EXAMPLE
X <- rexp(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MOP")
integralMoTBF(Px)
integralMoTBF(Px, 1.2)
integralMoTBF(Px, min(X), max(X))

## 2. EXAMPLE
X <- rnorm(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MOP")
iP <- integralMoTBF(Px); iP
plot(iP, xlim=range(X))
integralMoTBF(Px, 0.2)
integralMoTBF(Px, min(X), max(X))

## 3. EXAMPLE
X <- rchisq(1000, df = 3)
Px <- univMoTBF(X, POTENTIAL_TYPE="MTE")
integralMoTBF(Px)
integralMoTBF(Px, 1)
integralMoTBF(Px, min(X), max(X))

## Not run: 
## 4. EXAMPLE
Px <- "1+x+5"
class(Px)
integralMoTBF(Px)
## Error in integralMoTBF(Px): "fx is not an 'motbf' function."

## End(Not run)

Description

Method to calculate the non-defined integral of an "motbf" object of 'mte' subclass.

Usage

integralMTE(fx)

Arguments

Value

The non-defined integral of the function.

See Also

univMoTBF for learning and integralMoTBF for a more complete function to get defined and non-defined integrals of class "motbf".

Examples

## 1. EXAMPLE
X <- rexp(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MTE")
integralMTE(Px)

## 2. EXAMPLE
X <- rnorm(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MTE")
integralMTE(Px)

## Not run: 
## 3. EXAMPLE
X <- rnorm(1000)
Px <- univMoTBF(X, POTENTIAL_TYPE="MOP")
integralMTE(Px)
## Error in integralMTE(Px): fx is an 'motbf' function but not 'mte' subclass.
class(Px)
subclass(Px)

## End(Not run)

Description

This function allows to check whether a node is discrete or not

Usage

is.discrete(node, bn)

Arguments

Value

is.discrete returns TRUE or FALSE depending on whether the node is discrete or not.

Examples

## Create a dataset
  # Continuous variables
  x <- rnorm(100)
  y <- rnorm(100)
  
  # Discrete variable
  z <- sample(letters[1:2],size = 100, replace = TRUE)
  
  data <- data.frame(C1 = x, C2 = y, D1 = z, stringsAsFactors = FALSE)
  
## Get DAG
  dag <- LearningHC(data)

## Learn BN
  bn <- MoTBFs_Learning(dag, data, POTENTIAL_TYPE = "MTE")

## Check wheter a node is discrete or not

  # Using its name
  is.discrete("D1", bn)
  
  # Using its index position
  is.discrete(3, bn)

Description

is.observed() checks whether a node belongs to the evidence set or not.

Usage

is.observed(node, evi)

Arguments

Value

This function returns TRUE if "node" is included in "evi", or, otherwise, FALSE.

Examples

## Data frame of the evidence set
  obs <- data.frame(lip = "1", alm2 = 0.5, stringsAsFactors=FALSE)
  
## Check if x is in obs
  is.observed("x", obs)

Description

is.root checks whether a node has parents or not.

Usage

is.root(node, dag)

Arguments

Value

is.root returns TRUE or FALSE depending on whether the node is root or not.

Examples

## Create a dataset
  # Continuous variables
  x <- rnorm(100)
  y <- rnorm(100)
  
  # Discrete variable
  z <- sample(letters[1:2],size = 100, replace = TRUE)
  
  data <- data.frame(C1 = x, C2 = y, D1 = z, stringsAsFactors = FALSE)
  
## Get DAG
  dag <- LearningHC(data)
  
## Check if a node is root
 is.root("C1", dag)

Description

Function to compute multivariate CDFs.

Usage

jointCDF(df, grid)

Arguments

Value

jointCDF() returns a vector.

Examples

## Create dataset with 2 variables
n = 2
size = 50
df <- as.data.frame(matrix(round(rnorm(size*n),2), ncol = n))

## Create grid dataset
npointsgrid <- 10
ranges <- sapply(df, range)
eg <- list()
for(i in 1: ncol(df)){
  eg[[i]] <- seq(ranges[1,i], ranges[2,i], length.out = npointsgrid)
}

x <- expand.grid(eg)

## Joint cumulative values
jointCDF(df = df, grid = x)

Description

Two functions for learning joint MoTBFs. The first one, parametersJointMoTBF(), gets the parameters by solving a quadratic optimization problem, minimizing the mean squared error between the empirical joint CDF and the estimated CDF. The density is obtained as the derivative od the estimated CDF. The second one, jointMoTBF(), fixes the equation of the joint function using the previously learned parameters and converting this "character" string into an object of class "jointmotbf".

Usage

parametersJointMoTBF(X, ranges = NULL, dimensions = NULL)

jointMoTBF(object)

Arguments

Value

parametersJointMoTBF() returns a list with the following elements: Parameters, which contains the computed coefficients of the resulting function; Dimension, which is a "numeric" vector containing the number of coefficients used for each variable; Range contains a "numeric" matrix with the domain of each variable, by columns; Iterations contains the number of iterations needed to solve the problem; Time contains the execution time.

jointMoTBF() returns an object of class "jointmotbf", which is a list whose only visible element is the analytical expression of the learned density. It also contains the other aforementioned elements, which can be retrieved using attributes()

Examples

## 1. EXAMPLE 
## Generate a multinormal dataset
data <- data.frame(X1 = rnorm(100), X2 = rnorm(100))

## Joint learnings
dim <- c(2,3)
param <- parametersJointMoTBF(X = data, dimensions = dim)

param$Parameters
length(param$Parameters)
param$Dimension
param$Range

P <- jointMoTBF(param)
P
attributes(P)
class(P)

###############################################################################
## MORE EXAMPLES ##############################################################
###############################################################################

## Generate a dataset
data <- data.frame(X1 = rnorm(100), X2 = rnorm(100), X3 = rnorm(100))

## Joint learnings
dim <- c(3,2,3)
param <- parametersJointMoTBF(X = data, dimensions = dim)

param$Parameters
length(param$Parameters) ## prod(dim)
param$Dimension
param$Range
param$Time

P <- jointMoTBF(param)
P
attributes(P)
class(P)

Description

Learn the structure of a hybrid Bayesian network using the hill climbing local search method.

Usage

LearningHC(dataset, numIntervals = NULL)

Arguments

Details

LearningHC() automatically converts non-numeric variables into factors before calling function hc() from the bnlearn package. LearningHC() can also be used to discretize the dataset, using the equal width method, before calling hc().

Value

The output is a "bn" object containing the learned graph.

See Also

hc

Examples

## Data
data(ecoli)
ecoli <- ecoli[,-1] ## Sequence Name

## DAG1
dag1 <- LearningHC(ecoli)
dag1
plot(dag1)

## DAG2
dag2 <- LearningHC(ecoli, numIntervals = 10)
dag2
plot(dag2)

Description

Learns a univariate MoTBF function using prior information.

Usage

learnMoTBFpriorInformation(
  priorData,
  data,
  s,
  POTENTIAL_TYPE,
  domain = range(data),
  coeffversion = 4,
  restrictDomain = TRUE,
  maxParam = NULL
)

Arguments

Value

A list with the elements

See Also

getCoefficients

Examples

## Data
X <- rnorm(15)

## Prior Data
priordata <- rnorm(5000)

## Test data
test <- rnorm(1000)
testData <- test[test>=min(X)&test<=max(X)]

## Learning
type <- "MOP" 
confident <- 3 ## confident <- 1,2,...,length(X)
f <- learnMoTBFpriorInformation(priorData = priordata, data = X, s = confident,
POTENTIAL_TYPE = type)
attributes(f)

## Log-likelihood
sum(log(as.function(f$dataFunction)(testData)))
sum(log(as.function(f$posteriorFunction)(testData))) ## best loglikelihood

Description

Computes the marginal densities from a "jointmotbf" object.

Usage

marginalJointMoTBF(P, var)

Arguments

Value

The marginal of a "jointmotbf" function. The result is an object of class "motbf".

See Also

jointMoTBF and evalJointFunction

Examples

## 1. EXAMPLE 
## Dataset with 2 variables
X <- data.frame(rnorm(100), rnorm(100))

## Joint function
dim <- c(4,3)
param <- parametersJointMoTBF(X, dimensions = dim)
P <- jointMoTBF(param)
P

## Marginal
marginalJointMoTBF(P, var = "x")
marginalJointMoTBF(P, var = 2)

##############################################################################
## MORE EXAMPLES #############################################################
##############################################################################

## Generate a dataset with 3 variables
data <- data.frame(rnorm(100), rnorm(100), rnorm(100))

## Joint function
dim <- c(2,1,3)
param <- parametersJointMoTBF(data, dimensions = dim)
P <- jointMoTBF(param)
nVariables(P)

## Marginal
marginalJointMoTBF(P, var="x")
marginalJointMoTBF(P, var="y")
marginalJointMoTBF(P, var="z")

Description

These functions fit mixtures of polynomials (MOPs). Least square optimization is used to minimize the quadratic error between the empirical cumulative distribution and the estimated one.

Usage

mop.learning(X, nparam, domain)

bestMOP(X, domain, maxParam = NULL)

Arguments

Details

mop.learning(): The returned value $Function is the only visible element which contains the algebraic expression. Using attributes the name of the others elements are shown and also they can be extracted with $. The summary of the function also shows all these elements.

bestMOP(): The first returned value $bestPx contains the output of the mop.learning() function with the number of parameters which gets the best BIC values, taking into account the BIC score to penalize the functions. It evaluates the two next functions, if the BIC score does not improve then the function with the last best BIC is returned.

Value

mop.lerning() returns a list of n elements:

bestMOP() returns a list including the polynomial function with the best BIC score, the number of parameters and an array with the BIC values of the evaluated functions.

See Also

univMoTBF A complete function for learning MOPs which includes extra options.

Examples

## 1. EXAMPLE 
data <- rnorm(1000)

## MOP with fix number of degrees
fx <- mop.learning(data, nparam=7, domain=range(data))
fx
hist(data, prob=TRUE, main="")
plot(fx, col=2, xlim=range(data), add=TRUE)

## Best MOP in terms of BIC
fMOP <- bestMOP(data, domain=range(data))
attributes(fMOP)
fMOP$bestPx
hist(data, prob=TRUE, main="")
plot(fMOP$bestPx, col=2, xlim=range(data), add=TRUE)

## 2. EXAMPLE
data <- rbeta(4000, shape1=1/2, shape2=1/2)

## MOP with fix number of degrees 
fx <- mop.learning(data, nparam=6, domain=range(data))
fx
hist(data, prob=TRUE, main="")
plot(fx, col=2, xlim=range(data), add=TRUE)

## Best MOP in terms of BIC
fMOP <- bestMOP(data, domain=range(data), maxParam=6)
attributes(fMOP)
fMOP$bestPx
attributes(fMOP$bestPx)
hist(data, prob=TRUE, main="")
plot(fMOP$bestPx, col=2, xlim=range(data), add=TRUE)

Description

This function checks whether the density functions of a MoTBF-BN are of type MTE or MOP.

Usage

motbf_type(bn)

Arguments

Value

A character string, specifying the subclass of MoTBF, i.e., either MTE or MOP.

Examples

## Dataset
  data("ecoli", package = "MoTBFs")
  data <- ecoli[,-c(1,9)]

## Get directed acyclic graph
  dag <- LearningHC(data)
  
## Learn bayesian network
  bn <- MoTBFs_Learning(dag, data = data, numIntervals = 4, POTENTIAL_TYPE = "MTE") 
  
## Get MoTBF sub-class
  motbf_type(bn)

Description

Random generation for mixtures of truncated basis functions defined in a specific domain. The inverse transform method is used.

Usage

rMoTBF(size, fx, domain = NULL)

inversionMethod(size, fx, domain = NULL, data = NULL)

Arguments

Value

rMoTBF() returns a "numeric" vector containing the simulated values. inversionMethod() returns a list with the simulated values and the results of the two-sample Kolmogorov-Smirnov test, as well as the plot of the CDFs of the original and simulated data.

See Also

integralMoTBF

Examples

## 1. EXAMPLE
## Data
X <- rnorm(1000, mean = 5, sd = 3)

## Learning
f <- univMoTBF(X, POTENTIAL_TYPE="MOP", nparam=10)
plot(f, xlim = f$Domain)

## Random sample
Y <- rMoTBF(size = 500, fx = f)
ks.test(X,Y)

## Plots
hist(Y, prob = TRUE, add = TRUE)

## 2. EXAMPLE 
## Data
X <- rweibull(5000, shape=2)

## Learning
f <- univMoTBF(X, POTENTIAL_TYPE="MOP", nparam=10)
plot(f, xlim = f$Domain)

## Random sample
inv <- inversionMethod(size = 500, fx = f, data = X)
attributes(inv)
inv$test
Y <- inv$sample 

## Plots
plot(f, xlim = f$Domain)
hist(Y, prob = TRUE, add = TRUE)

Description

Learn mixtures of truncated basis functions in a full hybrid network.

Usage

MoTBFs_Learning(
  graph,
  data,
  numIntervals,
  POTENTIAL_TYPE,
  maxParam = NULL,
  s = NULL,
  priorData = NULL
)

Arguments

Details

If the variable is discrete then it computes the probabilities and the size of each leaf. Children that have discrete parents have as many functions as configurations of the parents. Children that have continuous parents have as many functions as the number indicated in the argument "numIntervals" for each parent. Children that have mixed parents, combine both methods. The BIC criterion is used to decide the number of splitting points of the parent domains and to choose the number of basis functions used.

Value

A list of lists. Each list contains two elements

See Also

printBN and ecoli

Examples

## Dataset Ecoli
require(MoTBFs)
data(ecoli)
data <- ecoli[,-c(1)] ## remove variable sequence

## Directed acyclic graph
dag <- LearningHC(data)

## Learning BN
intervals <- 3
potential <- "MOP"
P1 <- MoTBFs_Learning(graph = dag, data = data, numIntervals = intervals, POTENTIAL_TYPE=potential,
maxParam = 5)
printBN(P1)

 ## Learning BN
intervals <- 4
potential <- "MTE"
P2 <- MoTBFs_Learning(graph = dag, data = data, numIntervals = intervals, POTENTIAL_TYPE=potential,
maxParam = 15)
printBN(P2)

Description

These functions fit mixtures of truncated exponentials (MTEs). Least square optimization is used to minimize the quadratic error between the empirical cumulative distribution function and the estimated one.

Usage

mte.learning(X, nparam, domain)

bestMTE(X, domain, maxParam = NULL)

Arguments

Details

mte.learning(): The returned value $Function is the only visible element which contains the algebraic expression. Using attributes the name of the others elements are shown and also they can be abstract with $. The summary of the function also shows all this elements.

bestMTE(): The first returned value $bestPx contains the output of the mte.learning() function with the number of parameters which gets the best BIC value, taking into account the Bayesian information criterion (BIC) to penalize the functions. It evaluates the two next functions, if the BIC doesn't improve then the function with the last best BIC is returned.

Value

mte.lerning() returns a list of n elements:

bestMTE() returns a list including the MTE function with the best BIC score, the number of parameters, the best BIC value and an array contained the BIC values of the evaluated functions.

See Also

univMoTBF A complete function for learning MoTBFs which includes extra options.

Examples

## 1. EXAMPLE
data <- rchisq(1000, df=3)

## MTE with fix number of parameters
fx <- mte.learning(data, nparam=7, domain=range(data))
hist(data, prob=TRUE, main="")
plot(fx, col=2, xlim=range(data), add=TRUE)

## Best MTE in terms of BIC
fMTE <- bestMTE(data, domain=range(data))
attributes(fMTE)
fMTE$bestPx
hist(data, prob=TRUE, main="")
plot(fMTE$bestPx, col=2, xlim=range(data), add=TRUE)

## 2. EXAMPLE
data <- rexp(1000, rate=1/3)

 ## MTE with fix number of parameters
fx <- mte.learning(data, nparam=8, domain=range(data))
## Message: The nearest function with odd number of coefficients 
hist(data, prob=TRUE, main="")
plot(fx, col=2, xlim=range(data), add=TRUE)

## Best MTE in terms of BIC
fMTE <- bestMTE(data, domain=range(data), maxParam=10)
attributes(fMTE)
fMTE$bestPx
attributes(fMTE$bestPx)
hist(data, prob=TRUE, main="")
plot(fMTE$bestPx, col=2, xlim=range(data), add=TRUE)

Description

Computes the new domain of two datasets.

Usage

newRangePriorData(fPI, priorData, N, domain, s, POTENTIAL_TYPE)

Arguments

Value

A "numeric" array which contains the new domain of the prior function.

Examples

## Data
X <- rnorm(15)

## Prior Data
priordata <- rnorm(5000)

## Learning
type = "MTE" 
fPrior <- univMoTBF(priordata, POTENTIAL_TYPE = type)

## New range
confident <- 5 ## confident <- 1,2,...,length(X)
domain <- range(X)
N <- length(X)
newRange <- newRangePriorData(fPrior, priorData = priordata, N = N,
domain = domain, s = confident, POTENTIAL_TYPE = type)
newRange

Description

Compute the number of variables which are in a jointmotbf object.

Usage

nVariables(P)

Arguments

Value

A "character" vector with the names of the variables in the function.

Examples

# 1. EXAMPLE
## Generate a dataset
data <- data.frame(X1 = rnorm(100), X2 = rnorm(100))

## Joint function
dim <-c(3,2)
param <- parametersJointMoTBF(data, dimensions = dim)
P <- jointMoTBF(param)
P

## Variables
nVariables(P)

##############################################################################
## MORE EXAMPLES #############################################################
##############################################################################

## Generate a dataset
data <- data.frame(X1 = rnorm(100), X2 = rnorm(100), X3 = rnorm(100))

## Joint function
dim <- c(2,1,3)
param <- parametersJointMoTBF(data, dimensions = dim)
P <- jointMoTBF(param)

## Variables
nVariables(P)

Description

This function returns a data.frame of dimension '1xn' containing the values of the 'n' parents of a 'node' of interest. Use this function if you have a random sample and an observed sample with information about the parents. The values of the parents are obtained from the evidence set unless they are not observed. In this case, the values are taken from the random sample.

Usage

parentValues(node, bn, obs, rdf)

Arguments

Value

A data.frame containing the values of the parents of 'node'.

Examples

## Dataset
  data("ecoli", package = "MoTBFs")
  data <- ecoli[,-c(1,9)]

## Get directed acyclic graph
  dag <- LearningHC(data)
  
## Learn bayesian network
  bn <- MoTBFs_Learning(dag, data = data, numIntervals = 4, POTENTIAL_TYPE = "MTE")
  
## Specify the evidence set
  obs <- data.frame(lip = "1", alm1 = 0.5, stringsAsFactors=FALSE)
  
## Create a random sample
  contData <- data[ ,which(lapply(data, is.numeric) == TRUE)]
  fx <- lapply(contData, univMoTBF, POTENTIAL_TYPE = "MTE")
  disData <- data[ ,which(lapply(data, is.numeric) == FALSE)]
  conSample <- lapply(fx, rMoTBF, size = 1)
  disSample <- lapply(unique(disData), sample, size = 1)
  
  rdf <- as.data.frame(list(conSample,disSample), stringsAsFactors = FALSE)
  
## Get the values of the parents of node "alm2"
  parentValues("alm2", bn, obs, rdf)

Description

PLot the perpective and the contour plots for joint MoTBF functions.

Usage

## S3 method for class 'jointmotbf'
plot(
  x,
  type = "contour",
  ranges = NULL,
  orientation = c(5, -30),
  data = NULL,
  filled = TRUE,
  ticktype = "simple",
  ...
)

Arguments

Value

A plot of the joint MoTBF.

See Also

jointMoTBF

Examples

## 1 .EXAMPLE
## Dataset
X <- data.frame(rnorm(500), rnorm(500))

## Joint function
dim <- c(3,3) 
param1 <- parametersJointMoTBF(X, dimensions = dim)
P <- jointMoTBF(param1)
P

## Plots
plot(P)
plot(P, type = "perspective", orientation = c(90,0))

#############################################################################
## MORE EXAMPLES ############################################################
#############################################################################

## Dataset
X <- data.frame(rnorm(200,2), rexp(200, 1))

## Joint function
dim <- c(4,5)
param2 <- parametersJointMoTBF(X, dimensions = dim)
P <- jointMoTBF(param2)
P

## Plots
plot(P)
plot(P, filled = FALSE, data = X)
plot(P, type = "perspective", orientation = c(10,180))

Description

Draws an 'motbf' function.

Usage

## S3 method for class 'motbf'
plot(x, xlim = 0:1, ylim = NULL, type = "l", ...)

Arguments

Value

A plot of the specificated function.

Examples

## 1. EXAMPLE 
## Data
X <- rexp(2000)

## Learning
f1 <- univMoTBF(X, POTENTIAL_TYPE = "MOP"); f1
f2 <- univMoTBF(X, POTENTIAL_TYPE = "MTE", maxParam = 10); f2
f3 <- univMoTBF(X, POTENTIAL_TYPE = "MOP", nparam=10); f3
## Plots
plot(NULL, xlim = range(X), ylim = c(0,0.8), xlab="X", ylab="density")
plot(f1, xlim = range(X), col = 1, add = TRUE)
plot(f2, xlim = range(X), col = 2, add = TRUE)
plot(f3, xlim = range(X), col = 3, add = TRUE)
hist(X, prob = TRUE, add= TRUE)

## 2. EXAMPLE 
## Data
X <- c(rnorm(2000, mean = -3),rnorm(2000, mean = 3))

## Learning
f1 <- univMoTBF(X, POTENTIAL_TYPE = "MOP"); f1
f2 <- univMoTBF(X, POTENTIAL_TYPE = "MTE"); f2
## Plots
plot(NULL, xlim = range(X), ylim = c(0,0.20), xlab="X", ylab="density")
plot(f1, xlim = range(X), col = 2, add = TRUE)
plot(f2, xlim = range(X), col = 4, add = TRUE)
hist(X, prob = TRUE, add= TRUE)

Description

Plot conditional MoTBF densities.

Usage

plotConditional(
  conditionalFunction,
  data,
  nameChild = NULL,
  points = FALSE,
  color = NULL,
  ...
)

Arguments

Details

If the number of parents is greater than one, then the error message "It is not possible to plot the conditional function." is reported.

Value

A plot of the conditional density function.

See Also

conditionalMethod

Examples

## Data
X <- rnorm(1000)
Y <- rnorm(1000, mean=X)
data <- data.frame(X=X,Y=Y)
cov(data)

## Conditional Learning
parent <- "X"
child <- "Y"
intervals <- 5
potential <- "MTE"
P <- conditionalMethod(data, nameParents=parent, nameChild=child, 
numIntervals=intervals, POTENTIAL_TYPE=potential)
plotConditional(conditionalFunction=P, data=data)
plotConditional(conditionalFunction=P, data=data, points=TRUE)

Description

Delete rows of a dataset wich contains anomalous values.

Usage

preprocessedData(data, strangeElements)

Arguments

Description

Prints the content of a hybrid Bayesian network

Usage

printBN(MoTBF.BN)

Arguments

Value

The results of the fitted functions in the full network.

See Also

MoTBFs_Learning

Examples

## Dataset Ecoli
require(MoTBFs)
data(ecoli)
data <- ecoli[,-c(1)] ## remove variable sequence

## Directed acyclic graph
dag <- LearningHC(data)

## Learning BN
intervals <- 3
potential <- "MOP"
P <- MoTBFs_Learning(graph = dag, data = data, numIntervals = intervals, POTENTIAL_TYPE=potential,
maxParam = 15)
printBN(P)

Description

Print the description of an MoTBF demnsity for one variable conditional on another variable.

Usage

printConditional(conditionalFunction)

Arguments

Value

The results of the conditional function are shown.

See Also

conditionalMethod

Examples

## Data
X <- rexp(500)
Y <- rnorm(500, mean=X)
data <- data.frame(X=X,Y=Y)
cov(data)

## Conditional Learning
parent <- "X"
child <- "Y"
intervals <- 5
potential <- "MOP"
P <- conditionalMethod(data, nameParents=parent, nameChild=child, 
numIntervals=intervals, POTENTIAL_TYPE=potential)
printConditional(P)

Description

Prints the univariate and conditional distributions of a discrete BN.

Usage

printDiscreteBN(BN)

Arguments

Value

The results are shown on the screen.

Description

Compute the probabilities of a discrete variable from a dataset.

Usage

probDiscreteVariable(stateNames, Variable)

Arguments

Value

A list of "numeric" arrays:

See Also

discreteVariablesStates

Examples

## Discrete Variable
data <- data.frame(X=rep(c("yes", "no", "maybe"), 500))
data <- discreteVariables_as.character(data, "X")
n <- nrow(data)

## Probabilities
s <- discreteVariablesStates(namevariables="X", discreteData=data)
states <- s[[1]]$states
p <- probDiscreteVariable(stateNames=states, Variable=data$X)
p

Description

The function r.data.frame() initializes a data frame with as many columns as nodes in the MoTBF-network. It also asings each column its data type, i.e., numeric or character. In the case of character columns, the states of the variable are extracted from the "bn" argument and included as levels.

Usage

r.data.frame(bn, dag)

Arguments

Value

An object of class "data.frame", which contains the data type of each column and has no rows.

Examples

## Create a dataset
  # Continuous variables
  x <- rnorm(100)
  y <- rnorm(100)
  
  # Discrete variable
  z <- sample(letters[1:2],size = 100, replace = TRUE)
  
  data <- data.frame(C1 = x, C2 = y, D1 = z, stringsAsFactors = FALSE)
  
## Get DAG
  dag <- LearningHC(data)
  
## Learn a BN
  bn <- MoTBFs_Learning(dag, data, POTENTIAL_TYPE = "MTE")
  
## Initialize a data.frame containing 3 columns (x, y and z) with their attributes.
  r.data.frame(bn, dag)

Description

A collation of function to reescale an MoTBF function to the original offset and scale. This is useful when data was standardized previously to learning.

Usage

rescaledMoTBFs(fx, data)

rescaledMOP(fx, data)

ToStringRe_MOP(parameters, data)

rescaledMTE(fx, data)

ToStringRe_MTE(parameters, data, num = 5)

meanMOP(fx)

Arguments

Value

An "motbf" function of the original data.

See Also

univMoTBF

Examples

## 1. EXAMPLE
X <- rchisq(1000, df = 8) ## data
modX <- scale(X) ## scale data

## Learning
f <- univMoTBF(modX, POTENTIAL_TYPE = "MOP", nparam=10) 
plot(f, xlim = range(modX), col=2)
hist(modX, prob = TRUE, add = TRUE)

## Rescale
origF <- rescaledMoTBFs(f, X) 
plot(origF, xlim = range(X), col=2)
hist(X, prob = TRUE, add = TRUE)
meanMOP(origF) 
mean(X)

## 2. EXAMPLE 
X <- rweibull(1000, shape = 20, scale= 10) ## data
modX <- as.numeric(scale(X)) ## scale data

## Learning
f <- univMoTBF(modX, POTENTIAL_TYPE = "MTE", nparam = 9) 
plot(f, xlim = range(modX), col=2, main="")
hist(modX, prob = TRUE, add = TRUE)

## Rescale
origF <- rescaledMoTBFs(f, X) 
plot(origF, xlim = range(X), col=2)
hist(X, prob = TRUE, add = TRUE)

Description

Generate a multivariate normal data vector taking into account the real data and the relationships with other variables in the dataset.

Usage

rnormMultiv(n, dataParents, dataChild)

Arguments

Value

A "numeric" vector giving the prior data values.

See Also

generateNormalPriorData

Examples

## Data
data(ecoli)
data <- ecoli[,-c(1,9)] ## remove sequece.name and class

## DAG
dag <- LearningHC(data)
plot(dag)
getChildParentsFromGraph(dag)

## 1. Random sample
parents <- "mcg"
child <- "alm1"
n <- 1000
rnormMultiv(n, dataParents = data.frame(data[,parents]), dataChild = data[,child])

## 2. Random sample
parents <- "alm1"
child <- "aac"
n <- 256
rnormMultiv(n, dataParents = data.frame(data[,parents]), dataChild = data[,child])

Description

This function generates a sample from conditional MoTBFs.

Usage

sample_MoTBFs(bn, dag, obs = NULL, size, force_size = T)

Arguments

Value

A data.frame containing the generated sample.

Examples

## Dataset
  data("ecoli", package = "MoTBFs")
  data <- ecoli[,-c(1,9)]

## Get directed acyclic graph
  dag <- LearningHC(data)
  
## Learn bayesian network
  bn <- MoTBFs_Learning(dag, data = data, numIntervals = 4, POTENTIAL_TYPE = "MTE")
  
## Specify the evidence set 
  obs <- data.frame(lip = "0.48", alm1 = 0.55, gvh = 1, stringsAsFactors=FALSE)
  
## Get the conditional sample
  sample_MoTBFs(bn, dag, obs, size = 10)

Description

Collection of functions for detecting the subclass of an "motbf" object. It can be "mop" or "mte".

Usage

is.mte(fx)

is.mop(fx)

subclass(fx)

Arguments

Value

is.mte and is.mop return a logical value, TRUE if it is an "motbf" object of the subclass "mte" or "mop", respectly; or FALSE otherwise. subclass returns a "character" string, "mte" or "mop".

See Also

univMoTBF

Examples

## MOP Function
X <- rnorm(1000)
P <- univMoTBF(X, POTENTIAL_TYPE="MOP")
is.mop(P)
subclass(P)

## MTE Function
X <- rchisq(1000, df=4)
P <- univMoTBF(X, POTENTIAL_TYPE="MTE")
is.mte(P)
subclass(P)

Description

Collection of functions for subsetting a "data.frame" by rows or columns, and to create training and test partitions.

Usage

TrainingandTestData(data, percentage_test, discreteVariables = NULL)

newData(data, nameX, nameY)

splitdata(data, nameVariable, min, max)

Arguments

Value

TrainingandTestData() returns a list of 2 elements containing the train and test datasets. newData() and splitdata() return a subset of variables or observations, respectively.

Examples

## Dataset
X <- rnorm(1000)
Y <- rchisq(1000, df = 8)
Z <- rep(letters[1:10], times = 1000/10)
data <- data.frame(X = X, Y = Y, Z = Z)
data <- discreteVariables_as.character(dataset = data, discreteVariables ="Z")

## Training and Test Datasets
TT <- TrainingandTestData(data, percentage_test = 0.2)
TT$Training
TT$Test

## Subset Dataset
newData(data, nameX = "X", nameY = "Z")
splitdata(data, nameVariable = "X", min = 2, max= 3)