Type: Package
Title: Learning Hybrid Bayesian Networks using Mixtures of Truncated Basis Functions
Version: 1.4.1
Author: Inmaculada Pérez-Bernabé, Antonio Salmerón, Thomas D. Nielsen, Ana D. Maldonado
Maintainer: Ana D. Maldonado <ana.d.maldonado@ual.es>
Description: Learning, manipulation and evaluation of mixtures of truncated basis functions (MoTBFs), which include mixtures of polynomials (MOPs) and mixtures of truncated exponentials (MTEs). MoTBFs are a flexible framework for modelling hybrid Bayesian networks (I. Pérez-Bernabé, A. Salmerón, H. Langseth (2015) <doi:10.1007/978-3-319-20807-7_36>; H. Langseth, T.D. Nielsen, I. Pérez-Bernabé, A. Salmerón (2014) <doi:10.1016/j.ijar.2013.09.012>; I. Pérez-Bernabé, A. Fernández, R. Rumí, A. Salmerón (2016) <doi:10.1007/s10618-015-0429-7>). The package provides functionality for learning univariate, multivariate and conditional densities, with the possibility of incorporating prior knowledge. Structural learning of hybrid Bayesian networks is also provided. A set of useful tools is provided, including plotting, printing and likelihood evaluation. This package makes use of S3 objects, with two new classes called 'motbf' and 'jointmotbf'.
Depends: R (≥ 3.2.0)
Imports: quadprog, lpSolve, bnlearn, methods, ggm, Matrix
Encoding: UTF-8
License: LGPL-3
NeedsCompilation: yes
Repository: CRAN
Packaged: 2022-04-18 13:15:36 UTC; amaldonado
Date/Publication: 2022-04-18 16:34:30 UTC
RoxygenNote: 7.1.2

Computing the BIC score of an MoTBF function

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

Px

A function of class "motbf".

X

A "numeric" vector with the data to evaluate.

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)

BIC score for multiple functions

Description

Compute the BIC score using more than one probability functions.

Usage

BICMultiFunctions(Px, X)

Arguments

Px

A list of objects of class "motbf".

X

A list with as many "numeric" vectors as densities in Px, used to compute the BIC score for each density.

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)

Class "jointmotbf"

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

x

Preferably, a list containing an expression and other posibles elements like a "numeric" matrix with the domain of the variables, the dimension of the variables, the number of iterations needed to solve the optimization problem, among others. Any R object can be entered, but the utility of this function is not to transform objects of other classes into objects of class "jointmotbf".

...

Additional arguments, not needed by these methods.

class

By default is "jointmotbf".

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)

Class "motbf"

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

x

Preferably, a list containing an 'mte' or 'mop' univariate expression and other posibles elements like a "numeric" vector with the domain of the variable, the number of iterations needed to solve the optimization problem, among others. Any R object can be entered, but the utility of this function is not to transform objects of other classes into objects of class "motbf".

...

Additional arguments, not needed for these methods.

class

By default is "motbf".

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)

Score-based hybrid Bayesian Network structure learning

Description

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

Usage

LearningHC(dataset, numIntervals = NULL)

Arguments

dataset

A dataset with discrete and continuous variables. If the discrete variables are not of class "factor", they are automatically converted.

numIntervals

A "numeric" value indicating the number of categories used when discretizing a continuous variable, corresponding to intervals of equal width. By default it is NULL, meaning that the continuous variables are not discretized.

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)

Random generation for MoTBF distributions

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

size

A non-negative integer indicating the number of records to generate.

fx

An object of class "motbf".

domain

A "numeric" vector indicating the lower and upper limits to sample from. If not specified, the range is taken from the object fx.

data

A "numeric" vector to be compared with the simulated sample. By default, it is NULL; otherwise, the empirical cumulative distributions of both the data and the simulated sample are plotted and the Kolmogorov Smirnov test is used to test whether or not both samples can be considered to be drawn from the same distribution.

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)

Learning hybrid BNs with MoTBFs

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

graph

A network of the class "bn", "graphNEL" or "network".

data

An object of class "data.frame"; it can contain continuous and discrete variables.

numIntervals

A positive integer indicating the maximum number of intervals for splitting the domain of the continuous parent variables.

POTENTIAL_TYPE

A "character" string, either MOP or MTE, corresponding to the type of basis function.

maxParam

A positive integer which indicates the maximum number of coefficients in the function. If specified, the output is the function which gets the best BIC with, at most, this number of parameters. By default, it is set to NULL.

s

A "numeric" value which specifies the expert confidence in the prior knowledge. This argument takes values on the interval [0, N], where N is the sample size, and is used to synchronize the support of the prior knowledge and the sample. By default, it is NULL, and must be modified only if prior information is to be incorporated to the fits.

priorData

An object of class "data.frame", corresponding to the prior information.

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

Child

A "charater" string which contains the name of the child variable.

functions

A list of three elements: the name of the parents; a "numeric" vector indicating the interval of the parent; and the fitted function in this interval.

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)

Subclass "motbf" Functions

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

fx

A function of the class "motbf".

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)

Upper bound of the loglikelihood

Description

Computes an upper bound of the expected loglikelihood of a dataset given a randomly generated MoTBF density.

Usage

UpperBoundLogLikelihood(f, data, min, max)

Arguments

f

A function to evaluate of class "character", "motbf" or others.

data

A "numeric" array which contains the values to evaluate.

min

A "numeric" value giving the lower limit of the domain.

max

A "numeric" value giving the upper limit of the domain.

Value

A "numeric" value which is the log-likelihood of the evaluated ramdom function.

See Also

getNonNormalisedRandomMoTBF

Examples


data <- rnorm(20)
f <- getNonNormalisedRandomMoTBF(degree = 8, POTENTIAL_TYPE = "MOP")
UpperBoundLogLikelihood(f, data, min = -2.5, max = 3.2)

data <- rexp(20)
f <- getNonNormalisedRandomMoTBF(degree = 8, POTENTIAL_TYPE = "MTE")
UpperBoundLogLikelihood(f, data, min = 0, max = 5)

Coerce a "jointmotbf" Object to a Function

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

x

An object of class "joinmotbf".

...

Further arguments to be passed to or from the method. Not necessary for this method.

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))

Coerce an "motbf" object to a Function

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

x

An object of class "motbf".

...

Further arguments to be passed to or from the method. Not necessary for this method.

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)

Parameters to MOP String

Description

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

Usage

asMOPString(parameters)

Arguments

parameters

A "numeric" vector containing the coefficients.

Value

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

Examples


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

param <- 3.4
asMOPString(param)

Converting MTEs to strings

Description

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

Usage

asMTEString(parameters, num = 5)

Arguments

parameters

A "numeric" vector containing the coefficients.

num

A "numeric" value which contains the denominator of the coefficient in the exponential.

Value

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

Examples


param <- -5.8
asMTEString(param)

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

Remove Objects from Memory

Description

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

Usage

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

Arguments

envir

The currently active environment; by default It is the gloval environment.

n

Number of garbage collection repetitions; by default n = 2.

Examples

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

Coefficients of a "jointmotbf" object

Description

Extracts the parameters of a joint MoTBF density.

Usage

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

Arguments

object

An MoTBF function.

...

Other arguments, unnecessary for this function.

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)

Extract coefficients from MOPs

Description

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

Usage

coeffMOP(fx)

coeffPol(fx)

Arguments

fx

An "motbf" function of subclass 'mop'.

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)

Extract the coefficients of an MoTBF

Description

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

Usage

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

Arguments

object

An object of class motbf.

...

other 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)

Extracting the coefficients of an MTE

Description

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

Usage

coeffMTE(fx)

coeffExp(fx)

Arguments

fx

An "motbf" function of subclass 'mte'.

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)

Degree Function

Description

Compute the degree for each term of a joint CDF.

Usage

coefExpJointCDF(dimensions)

Arguments

dimensions

A "numeric" vector including the number of parameters of each variable.

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)

Learning conditional MoTBF densities

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

data

An object of class "data.frame".

nameParents

A "character" vector containing the names of the parent variables.

nameChild

A "character" string containing the name of the child variable.

numIntervals

A positive integer indicating the maximum number of intervals for splitting the domain of the parent variables.

POTENTIAL_TYPE

A "character" string, either MOP or MTE, corresponding to the type of basis function.

maxParam

A positive integer which indicates the maximum number of coefficients in the function. If specified, the output is the function which gets the best BIC with, at most, this number of parameters. By default, it is set to NULL.

s

A "numeric" value indicating the expert's confidence in the prior knowledge. This argument takes values on the interval [0, N], where N is the sample size, and is used to synchronize the support of the prior knowledge and the sample. By default, it is NULL, and must be modified only if prior information is to be incorporated in the learning process.

priorData

An object of class "data.frame", corresponding to the prior information.

domainChild

A "numeric" vector with the range of the child variable.

domainParents

An object of class "matrix" with the range of the parent variables, or a "numeric" vector if there is only one parent.

mm

One of the inputs and the output of the recursive internal function "conditional".

conditionalfunction

The output of the internal function learn.tree.Intervals.

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)

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

Data pre-processing utilities

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

dataset

A dataset of class "data.frame". Tha variables of the dataset can be discrete and continuous.

discreteVariables

A "character" array with the names of the discrete variables.

numIntervals

Number of bins used to discretize the continuous variables.

factor

A boolean value indicating if the variables should be considered as "factor" or as "character". By default it is set to FALSE.

binary

By default it is set to FALSE, indicating that only binary entries are used for continuous variables; a TRUE value means that binary entries are used to discretize the full dataset taking into account the states the discrete variables.

namevariables

an array with the names of the varibles.

discreteData

A discretized dataset of class "data.frame".

DiscreteVariablesStates

The output of the function discreteVariablesStates.

X

A "numeric" vector with the data values of a continuous variable.

scale

A "numeric" vector (when it refers to a single variable) or a "list" containing the name(s) of the variable(s) and the scale value.

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)

Derivative of a MOP

Description

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

Usage

derivMOP(fx)

Arguments

fx

An "motbf" object of the 'mop' subclass.

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)

Derivating MTEs

Description

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

Usage

derivMTE(fx)

Arguments

fx

An "motbf" object of the 'mte' subclass.

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)

Derivating MoTBFs

Description

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

Usage

derivMoTBF(fx)

Arguments

fx

An object of class "motbf".

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)

Dimension of MoTBFs

Description

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

Usage

dimensionFunction(P)

Arguments

P

An object of class "motbf" and subclass 'mop' or "jointmotbf".

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)

Get the states of all discrete nodes from a MoTFB-BN

Description

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

Usage

discreteStatesFromBN(bn, dag)

Arguments

bn

A list of lists obtained from MoTBFs_Learning.

dag

A network of class "bn".

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)

Data set Ecoli: Protein Localization Sites

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

Evaluation of joint MoTBFs

Description

Evaluates a "jointmotbf" object at a specific point.

Usage

evalJointFunction(P, values)

Arguments

P

A "jointmotbf" object.

values

A list with the name of the variables equal to the values to be evaluated.

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)

Find fitted conditional MoTBFs

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

node

A character string, representing the tardet variable.

bn

A list of lists obtained from MoTBFs_Learning, containing the conditional functions.

evi

A data.frame of dimension '1xn' that contains the values of the 'n' parents of the target node. This argument can be NULL if "node" is a root node.

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)

Forward Sampling

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

bn

A list of lists obtained from the function MoTBFs_Learning.

dag

An object of class "bn", representing the directed acyclic graph.

target

A character string equal to the name of the variable of interest.

evi

A data.frame containing the observed variables.

size

A positive integer giving the number of instances to be generated.

...

Optional arguments passed on to the univMoTBF function. evalRange, nparam and maxParam can be specified. POTENTIAL_TYPE is taken from the 'bn' object.

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)

Prior data generation

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

graph

A network of the class "bn", "graphNEL" or "network".

data

An object of class "data.frame" containing the continuous variables in the dataset.

size

A positive integer indicating the number of records to generate for each variable in the dataset.

means

A "numeric" vector with the average of the variables whose prior information is available. The names in the vector must be the same as the names of the variables in the data.frame.

deviations

A "numeric" vector with the standard deviations of the variables whose prior information is available. The names of the vector must be the same as the names of the variables in the data.frame. If not specified, the standard deviation of each variable is computed from 'data'.

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)

Get the list of relations in a graph

Description

Compute the parents of each variable in the graph.

Usage

getChildParentsFromGraph(graph, nameVars = NULL)

Arguments

graph

A directed acyclic graph of the class "graphNEL", "network" or "bn".

nameVars

A character array containing the names of the variables in the graph. This parameter is only used when graph is of class "network".

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)

Get the coefficients

Description

Compute the coefficients for the linear opinion pool

Usage

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

Arguments

fPI

The function fitted to the prior data, of class "motbf".

rangeNewPriorData

An array of length 2 with the new domain of the prior function.

fD

The function fitted to the original data, of class "motbf".

data

A "numeric" array which contains the sample.

domain

A "numeric" array with the domain of the data density function.

coeffversion

A "numeric" value between 1--4 which contains the used version for computing the coefficients in the linear opinion pool to combine the prior function and the data function. By default coeffversion = "4" is used, so the combination depends on the goodness of the model versus another random positive MoTBF model.

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)

Ramdom MoTBF

Description

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

Usage

getNonNormalisedRandomMoTBF(degree, POTENTIAL_TYPE = "MOP")

Arguments

degree

A "numeric" value containing the degree of the random function.

POTENTIAL_TYPE

A "character" string specifying the posibles potential types, must be one of "MOP" or "MTE".

Value

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

Examples


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

BIC scxore and log-likelihood

Description

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

Usage

getlogLikelihoodDiscreteBN(discreteBN)

getBICDiscreteBN(discreteBN, sameData = FALSE)

Arguments

discreteBN

A list of multiples lists. Each list contains two entries, the probabilities and the size of the data which is in each leaf of the discrete tree.

sameData

A logical argument; FALSE means that different datasets were used for learning.

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)

BIC of a hybrid BN

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

MoTBF.BN

The output of the 'MoTBF_Learning' method.

data

The dataset of class data.frame.

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

Integration with MoTBFs

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

P

A "jointmotbf" object.

var

A "character" vector containing the name of the variables that will be integrated out. Instead of the names, the position of the variables can be given. By default it's NULL then all the variables are integrated out.

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"))

Integration of MOPs

Description

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

Usage

integralMOP(fx)

Arguments

fx

An "motbf" object of subclass 'mop'.

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)

Integrating MTEs

Description

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

Usage

integralMTE(fx)

Arguments

fx

An "motbf" object of subclass 'mte'.

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)

Integrating MoTBFs

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

fx

An object of class "motbf".

min

The lower integration limit. By default it is NULL.

max

The upper integration limit. By default it is NULL.

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)

Check discreteness of a node

Description

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

Usage

is.discrete(node, bn)

Arguments

node

A character (name of node) or numeric (index of node in the bn list) input.

bn

A list of lists obtained from MoTBFs_Learning.

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)

Observed Node

Description

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

Usage

is.observed(node, evi)

Arguments

node

A character string, matching the node's name.

evi

A data.frame of the evidence set.

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)

Root nodes

Description

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

Usage

is.root(node, dag)

Arguments

node

A character string indicating the name of the node.

dag

An object of class "bn".

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)

Joint MoTBFs CDFs

Description

Function to compute multivariate CDFs.

Usage

jointCDF(df, grid)

Arguments

df

The dataset as an object of class data.frame.

grid

a data.frame with the selected data points where the objective function will be evaluated when optimizing the parameters.

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)

Joint MoTBF density learning

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

X

A dataset of class "data.frame".

ranges

A "numeric" matrix containing the range of the varibles used to fit the function, where each column corresponds to a variable. If not specified, the range of each variable is computed from the data.

dimensions

A "numeric" vector containing the number of parameters of each varible.

object

A list with the output of the function parametersJointMoTBF().

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)

Incorporating prior knowledge in the estimation process

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

priorData

A "numeric" vector which contains the prior information.

data

A "numeric" vector containing the observed data.

s

A "numeric" value which specifies the expert confidence in the prior knowledge. This argument takes values on the interval [0, N], where N is the sample size, and is used to synchronize the support of the prior knowledge and the sample.

POTENTIAL_TYPE

A "character" string, either MOP or MTE, corresponding to the type of basis function.

domain

A "numeric" vector which contains the bounding values to fit the function. By default, it is the range of the data.

coeffversion

A "numeric" value between 1--4 which contains the used version for computing the coefficients of the linear opinion pool to combine the prior function and the data function. By default, coeffversion = "4" is used, so the combination depends on the goodness of the model versus another random model.

restrictDomain

A logical value. This argument allows to choose if the domain is used joining both domains, the prior one and the data domain or trimming them. By default, TRUE is used, so the domain will be trimmed.

maxParam

A positive integer which indicates the maximum number of coefficients in the function. If specified, the output is the function which gets the best BIC with, at most, this number of parameters. By default, it is set to NULL.

Value

A list with the elements

coeffs

An "numeric" vector with the two coefficients of the linear opinion pool

posteriorFunction

The final function after combining.

priorFunction

The fit of the prior data.

dataFunction

The fit of the original data.

rangeNewPriorData

A "numeric" vector which contains the final domain where the functions are defined.

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

Marginalization of MoTBFs

Description

Computes the marginal densities from a "jointmotbf" object.

Usage

marginalJointMoTBF(P, var)

Arguments

P

An object of class "jointmotbf", i.e., the joint density function.

var

The "numeric" position or the "character" name of the marginal variable.

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")

Fitting mixtures of polynomials

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

X

A "numeric" data vector.

nparam

Number of parameters of the function.

domain

A "numeric" containing the interval over which the function is defined.

maxParam

A "numeric" value indicating the maximum number of coefficients in the function. By default it is NULL, which means that the number of parameter is not limited. The output is the function which gets the best BIC (with at mostmaxParam parameters if not NULL).

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:

Function

An "motbf" object of the 'mop' subclass.

Subclass

'mop'.

Domain

The range where the function is defined to be a legal density function.

Iterations

The number of iterations that the optimization problem takes to minimize the errors.

Time

The CPU time employed.

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)

Type of MoTBF

Description

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

Usage

motbf_type(bn)

Arguments

bn

A list of lists obtained from the function MoTBFs_Learning.

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)

Fitting mixtures of truncated exponentials.

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

X

A "numeric" data vector.

nparam

Number of parameters of the resulting density function.

domain

A "numeric" containing the domain if the function to estimate.

maxParam

A "numeric" value indicating the maximum number of coefficients in the function. By default it is NULL; otherwise, the output is the function which gets the best BIC with at most this number of parameters.

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:

Function

An "motbf" object of the 'mte' subclass.

Subclass

'mte'.

Domain

The range where the function is defined to be a legal density function.

Iterations

The number of iterations that the optimization problem employed to minimize the errors.

Time

The CPU time consumed.

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)

Number of Variables in a Joint Function

Description

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

Usage

nVariables(P)

Arguments

P

An "motbf" object or a "jointmotbf" object.

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)

Redefining the Domain

Description

Computes the new domain of two datasets.

Usage

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

Arguments

fPI

The function fitted to the prior data, of class "motbf".

priorData

A "numeric" array with the values to be included as prior information.

N

A "numeric" value equal to the data size.

domain

A "numeric" array with the domain of the data density.

s

A "numeric" value which is the expert's confidence on the prior information. It is a number between 0 and the data size.

POTENTIAL_TYPE

A "character" string giving the potential of the model, i.e. "MOP" if the basis functions are polynomials, or "MTE" if they are exponentials.

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

Value of parent nodes

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

node

A character string that represents the node's name.

bn

A list of lists obtained from the function MoTBFs_Learning. It contains the conditional density functions of the bayesian network.

obs

A data.frame of dimension '1xm' containing an instance of the 'm' variables that belong to the evidence set.

rdf

A data.frame of dimension '1xk' containing an instance of the 'k' variables sampled from the bayesian network.

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)

Bidimensional plots for 'jointmotbf' objects

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

x

An object of class 'jointmotbf'.

type

A "character" string, either contour or perspective. It is set to "contour" by default.

ranges

A "numeric" matrix containing the domain of the variables, by columns, which is used to specify the plotting range.

orientation

A "numeric" vector indicating the perpective of the plot in degrees. By default, it is set to (5,-30).

data

An object of class "data.frame" containing two columns only. This argument is used to draw the points over the main plot. By default, it is set to NULL.

filled

A logical argument; it is only used if type = "contour". is active. By default, it is TRUE, so filled contours are plotted.

ticktype

A "character" string, either simple or detailed. By default, it is set to "simple", which draws just an arrow parallel to the axis to indicate direction of increase. In contrast, "detailed" draws normal ticks. This argument is only used in the "perspective" plot.

...

Further arguments to be passed to plot.

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))

Plots for 'motbf' objects

Description

Draws an 'motbf' function.

Usage

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

Arguments

x

An object of class 'motbf'.

xlim

The range to be encompassed by the x axis; by default 0:1.

ylim

The range of the y axix.

type

As for plot.

...

Further arguments to be passed as for plot.

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)

Plot Conditional Functions

Description

Plot conditional MoTBF densities.

Usage

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

Arguments

conditionalFunction

the output of function conditionalMethod. A list containing the the interval of the parent and the final conditional density (MTE or MOP).

data

An object of class data.frame, corresponding to the dataset used to fit the conditional density.

nameChild

A character string, corresponding to the name of the child variable in the conditional density. By default, it is NULL.

points

A logical value. If TRUE, the sample points are overlaid.

color

If not specified, a default palette is used.

...

Additional graphical parameters passed to filled.contour().

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)

Data cleaning

Description

Delete rows of a dataset wich contains anomalous values.

Usage

preprocessedData(data, strangeElements)

Arguments

data

A dataset of class "matrix" or "data.frame",

strangeElements

A "character" string which contains the elementes to remove.

BN printing

Description

Prints the content of a hybrid Bayesian network

Usage

printBN(MoTBF.BN)

Arguments

MoTBF.BN

The output of the method MoTBFs_Learning().

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)

Summary of conditional MoTBF densities

Description

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

Usage

printConditional(conditionalFunction)

Arguments

conditionalFunction

the output of the function conditionalMethod. A list with the interval of the parent and the final "motbf" density function fitted in each interval.

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)

Printing discrete Bayesian networks

Description

Prints the univariate and conditional distributions of a discrete BN.

Usage

printDiscreteBN(BN)

Arguments

BN

A discrete learning.

Value

The results are shown on the screen.

Probability distribution of discrete variables

Description

Compute the probabilities of a discrete variable from a dataset.

Usage

probDiscreteVariable(stateNames, Variable)

Arguments

stateNames

A "character" array indicating the states of the variable.

Variable

A "numeric" array containing the records of the variable.

Value

A list of "numeric" arrays:

coeff

Contains the probabilities.

sizeDataLeaf

Number of records in each leaf of the discrete tree.

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

Data frame initialization for forward sampling

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

bn

A list of lists obtained from the function MoTBFs_Learning.

dag

An object of class "bn", representing the graph of the bayesian network.

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)

Rescaling MoTBF functions

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

fx

A function of class "motbf" learned from a scaled data.

data

A "numeric" vector containing the original data (non standardizded).

parameters

A "numeric" vector with the coefficients to create the rescaled MoTBF.

num

A "numeric" value which contains the denominator of the coefficient in the exponential. By default it is 5.

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)

Multivariate Normal sampling

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

n

A "numeric" value which is the size of the prior data to generate.

dataParents

A data set of class "data.frame" giving the data of the set of coditional parent variables.

dataChild

A "numeric" vector containing the original data of the child variable.

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])

Sample generation from conditional MoTBFs

Description

This function generates a sample from conditional MoTBFs.

Usage

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

Arguments

bn

A list of lists obtained from the function MoTBFs_Learning.

dag

An object of class "bn", representing the directed acyclic graph.

obs

A data.frame containing the observed variables. This argument can be omitted if no variable is observed.

size

A non-negative integer giving the number of instances to be generated.

force_size

logical indicating if the sample must be of the size indicated. As a default, it is set to TRUE.

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)

Dataset subsetting

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

data

A dataset of class data.frame.

percentage_test

The proportion of data that goes to the test set (between 0 and 1).

discreteVariables

A character vector with the name of the discrete variables.

nameX

A character vector with the name of the child variable in the conditional method.

nameY

A character vector with the name of the parent variables in the conditional method.

nameVariable

A character vector with the name of the variable to be filtered.

min, max

Boundary values to filter out.

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)

Summary of a "jointmotbf" object

Description

Summarize a "jointmotbf" object by describing its main features.

Usage

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

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

Arguments

object

An object of class "jointmotbf".

...

further arguments passed to or from other methods.

x

An object of class "summary.jointmotbf".

Value

The summary of a "jointmotbf" object. It contains a list of elements with the most important information about the object.

See Also

parametersJointMoTBF and jointMoTBF

Examples

## 1. EXAMPLE
X <- rnorm(100)
Y <- rexp(100)
data <- data.frame(X, Y)
dim <- c(3,4)
param <- parametersJointMoTBF(data, dimensions=dim)
P <- jointMoTBF(param)
summary(P)
attributes(sP <- summary(P))
attributes(sP)
sP$Function
sP$Domain
sP$Iterations

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

X <- rnorm(100)
Y <- rexp(100)
Z <- rnorm(100, mean=1)
data <- data.frame(X, Y, Z)
dim <- c(3,2,4)
param <- parametersJointMoTBF(data, dimensions=dim)
P <- jointMoTBF(param)
summary(P)
attributes(sP <- summary(P))
sP$Function
sP$Domain
sP$Iterations

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

Summary of an "motbf" object

Description

Summarize an "motbf" object by describing its main features.

Usage

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

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

Arguments

object

An object of class "motbf".

...

further arguments passed to or from other methods.

x

An object of class "summary.motbf".

Value

The summary of an "motbf" object. It contains a list of elements with the most important information of the object.

See Also

univMoTBF

Examples

## Subclass 'MOP'
X <- rnorm(1000)
P <- univMoTBF(X, POTENTIAL_TYPE="MOP") ## or POTENTIAL_TYPE="MTE"
summary(P)
attributes(sP <- summary(P))
attributes(sP)
sP$Function
sP$Subclass
sP$Iterations

## Subclass 'MTE'
X <- rnorm(1000)
P <- univMoTBF(X, POTENTIAL_TYPE="MTE")
summary(P)
attributes(sP <- summary(P))
attributes(sP)
sP$Function
sP$Subclass
sP$Iterations

Data set Thyroid Disease (thyroid0387)

Description

This data set if one of the several databases about Thyroid avalaible at the UCI repository. The task is to detect is a given patient is normal (1) or suffers from hyperthyroidism (2) or hypothyroidism (3) .

Format

A data frame with 7200 rows, 21 variables and the class.

Details

Age

Age of the patient (0.01–0.97). Continuous variable.

Sex

Sex of the patient, 0 (Male) 1 (Female). Binary variable.

On_thyroxine

0 (FALSE) 1 (TRUE). Binary variable.

Query_on_thyroxine

0 (FALSE) 1 (TRUE). Binary variable.

On_antithyroid_medication

0 (FALSE) 1 (TRUE). Binary variable.

Sick

0 (FALSE) 1 (TRUE). Binary variable.

Pregnant

0 (FALSE) 1 (TRUE). Binary variable.

Thyroid_surgery

0 (FALSE) 1 (TRUE). Binary variable.

I131_treatment

0 (FALSE) 1 (TRUE). Binary variable.

Query_hypothyroid

0 (FALSE) 1 (TRUE). Binary variable.

Query_hyperthyroid

0 (FALSE) 1 (TRUE). Binary variable.

Lithium

0 (FALSE) 1 (TRUE). Binary variable.

Goitre

0 (FALSE) 1 (TRUE). Binary variable.

Tumor

0 (FALSE) 1 (TRUE). Binary variable.

Hypopituitary

0 (FALSE) 1 (TRUE). Binary variable.

Psych

0 (FALSE) 1 (TRUE). Binary variable.

TSH

amount of TSH (0.0–0.53). Continuous variable.

T3

amount of T3 (0.0005–0.18). Continuous variable.

TT4

amount of TT4 (0.002–0.6). Continuous variable.

T4U

amount of T4U (0.017–0.233). Continuous variable.

FTI

amount of FTI (0.002–0.642). Continuous variable.

Class

1 (normal) 2 (hyperthyroidism) 3 (hypothyroidism). Class variable.

Source

http://archive.ics.uci.edu/ml/datasets/Thyroid+Disease

Fitting MoTBFs

Description

Function for fitting univariate mixture of truncated basis functions. Least square optimization is used to minimize the quadratic error between the empirical cumulative distribution and the estimated one.

Usage

univMoTBF(
  data,
  POTENTIAL_TYPE,
  evalRange = NULL,
  nparam = NULL,
  maxParam = NULL
)

Arguments

data

A "numeric" vector.

POTENTIAL_TYPE

A "character" string specifying the potential type, must be either "MOP" or "MTE".

evalRange

A "numeric" vector that specifies the domain over which the model will be fitted. By default, it is NULL and the function is defined over the complete data range.

nparam

The exact number of basis functions to be used. By default, it is NULL and the best MoTBF is fitted taking into account the Bayesian information criterion (BIC) to score and select the functions. It evaluates the next two functions and, if the BIC value does not improve, the function with the best BIC score so far is returned.

maxParam

A "numeric" value which indicates the maximum number of coefficients in the function. By default, it is NULL; otherwise, the function which gets the best BIC score with at most this number of parameters is returned.

Value

univMoTBF() returns an object of class "motbf". This object is a list containing several elements, including its mathematical expression and other hidden elements related to the learning task. The processing time is one of the values returned by this function and it can be extracted by $Time. Although the learning process is always the same for a particular data sample, the processing can vary inasmuch as it depends on the CPU.

Examples

## 1. EXAMPLE
## Data
X <- rnorm(5000)

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

## Plots
hist(X, prob = TRUE, main = "")
plot(f1, xlim = range(X), col = 1, add = TRUE)
plot(f2, xlim = range(X), col = 2, add = TRUE)

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

## Log-likelihood
sum(log(as.function(f1)(Xtest)))
sum(log(as.function(f2)(Xtest)))

## 2. EXAMPLE
## Data
X <- rchisq(5000, df = 5)

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

## Plots
hist(X, prob = TRUE, main = "")
plot(f1, xlim = range(X), col = 3, add = TRUE)
plot(f2, xlim = range(X), col = 4, add = TRUE)

## Data test
Xtest <- rchisq(1000, df = 5)
## Filtered data test
Xtest <- Xtest[Xtest>=min(X) & Xtest<=max(X)]

## Log-likelihood
sum(log(as.function(f1)(Xtest)))
sum(log(as.function(f2)(Xtest)))