Package 'BiCausality' reference manual

Title:	Binary Causality Inference Framework
Description:	A framework to infer causality on binary data using techniques in frequent pattern mining and estimation statistics. Given a set of individual vectors S={x} where x(i) is a realization value of binary variable i, the framework infers empirical causal relations of binary variables i,j from S in a form of causal graph G=(V,E) where V is a set of nodes representing binary variables and there is an edge from i to j in E if the variable i causes j. The framework determines dependency among variables as well as analyzing confounding factors before deciding whether i causes j. The publication of this package is at Chainarong Amornbunchornvej, Navaporn Surasvadi, Anon Plangprasopchok, and Suttipong Thajchayapong (2023) <doi:10.1016/j.heliyon.2023.e15947>.
Authors:	Chainarong Amornbunchornvej [aut, cre]
Maintainer:	Chainarong Amornbunchornvej <[email protected]>
License:	MIT + file LICENSE
Version:	0.1.4
Built:	2025-02-03 04:54:33 UTC
Source:	https://github.com/darkeyes/bicausality

adjustmentProb function

Description

This function evaluates the P(Y=yflag|do(X=xflag)) given only marginal distributions using parent adjustment method.

Usage

adjustmentProb(EValHat, mat, yflag = 1, xflag = 1)
adjustmentProb(EValHat, mat, yflag = 1, xflag = 1)

Arguments

`EValHat`	is an adjacency matrix of weighted directed causal graph where edge weights are P(Y=yflag\|X=xflag) or probabilities of effect being 1 given cause being either 1 for positive association or 0 for negative association.
`mat`	is a matrix n by d where n is a number of transactions or samples and d is a number of dimensions.
`yflag`	is value set for Y in P(Y=yflag\|X=xflag,z) for the adjustment method.
`xflag`	is value set for X in P(Y=yflag\|X=xflag,z) for the adjustment method.

Value

This function returns an adjacency matrix of weighted directed causal graph where the edge weights are P(Y=yflag|do(X=xflag) ).

Examples

adjustmentProb(resC$CausalGRes$EValHat,mat)

adjustmentProb(resC$CausalGRes$EValHat,mat)

This function provides association signs (positive/negative association) inference between i and j. If there is a positive association, it implies i and j trend to have a similar value. For a negative association, however, i and j trend to have an opposite value.

Usage

assocSignTest(mat, i, j, z = c(), alpha = 0.05, IndpThs = 0.05, nboot = 100)
assocSignTest(mat, i, j, z = c(), alpha = 0.05, IndpThs = 0.05, nboot = 100)

Arguments

`mat`	is a matrix n by d where n is a number of transactions or samples and d is a number of dimensions.
`i`	is an ith dimension in `mat`.
`j`	is an jth dimension in `mat`.
`z`	is a conditioning d-dimensional vector on `mat`. Given k non-negative-bit positions of `z`, all k bit positions of samples in the subset of `mat` must have similar values with these bits.
`alpha`	is a significance threshold for hypothesis tests (Mann Whitney) that deploys for testing degrees of dependency, association direction, and causal direction. The default is 0.5.
`IndpThs`	is a threshold for the degree of dependency. In the independence test, to claim that any variables are dependent, the dependency degree must greater than this value significantly. The default is 0.05.
`nboot`	is a number of bootstrap replicates for bootstrapping deployed to infer confidence intervals and distributions for hypothesis tests. The default is 100.

Value

This function returns results of inference of association signs (positive/negative association) between i and j.

`bmean`	A mean of sign dependency degrees between variables i and j.
`confInv`	An `alpha`*100th percentile confidence interval of sign dependency degrees between variables i and j.
`testRes`	A Mann-Whitney hypothesis test result for an independence test between variables i and j. The null hypothesis is that the distributions of dependency degrees of i,j differ by a location shift of `IndpThs` and the alternative is that distributions of dependency degrees of i,j is shifted greater than `IndpThs`.

Examples

assocSignTest(mat=mat,i=1,j=2)
assocSignTest(mat=mat,i=1,j=2)

bin2dec function

Description

This function convertes a binary vector into its decimal value.

Usage

bin2dec(X)
bin2dec(X)

Arguments

`X`	is a binary vector where `X[i]` is the ith bit of vector.

Value

This function returns a decimal value of X.

Examples

bin2dec(X=c(1,1,1,0))

bin2dec(X=c(1,1,1,0))

bIndpTest function

Description

This function infers dependency for a pair of variables i,j with bootstrapping.

Usage

bIndpTest(
  mat,
  i,
  j,
  z = c(),
  alpha = 0.05,
  IndpThs = 0.05,
  nboot = 100,
  pflag = FALSE
)
bIndpTest(
  mat,
  i,
  j,
  z = c(),
  alpha = 0.05,
  IndpThs = 0.05,
  nboot = 100,
  pflag = FALSE
)

Arguments

`mat`	is a matrix n by d where n is a number of transactions or samples and d is a number of dimensions.
`i`	is an ith dimension in `mat`.
`j`	is an jth dimension in `mat`.
`z`	is a conditioning d-dimensional vector on `mat`. Given k non-negative-bit positions of `z`, all k bit positions of samples in the subset of `mat` must have similar values with these bits.
`alpha`	is a significance threshold for hypothesis tests (Mann Whitney) that deploys for testing degrees of dependency, association direction, and causal direction. The default is 0.5.
`IndpThs`	is a threshold for the degree of dependency. In the independence test, to claim that any variables are dependent, the dependency degree must greater than this value significantly. The default is 0.05.
`nboot`	is a number of bootstrap replicates for bootstrapping deployed to infer confidence intervals and distributions for hypothesis tests. The default is 100.
`pflag`	is a flag for printing progress message (TRUE). The default is FALSE (no printing).

Value

This function returns results of dependency inference between i and j.

`bmean`	A mean of dependency degrees between variables i and j.
`confInv`	An `alpha`*100th percentile confidence interval of dependency degrees between variables i and j.
`testRes`	A Mann-Whitney hypothesis test result for an independence test between variables i and j. The null hypothesis is that the distributions of dependency degrees of i,j differ by a location shift of `IndpThs` and the alternative is that distributions of dependency degrees of i,j is shifted greater than `IndpThs`.

Examples

bIndpTest(mat=mat,i=1,j=2)


bIndpTest(mat=mat,i=1,j=2)

bSCMCausalGraphFunc function

Description

This function infers a causal graph from a result of confounding factor filtering by bSCMdeConfoundingGraphFunc().

Usage

bSCMCausalGraphFunc(E1, Dboot, alpha = 0.05, SignThs = 0.05, CausalThs = 0.25)
bSCMCausalGraphFunc(E1, Dboot, alpha = 0.05, SignThs = 0.05, CausalThs = 0.25)

Arguments

`E1`	is an adjacency matrix of undirected graph after filtering associations without true causal directions from any confounding factor.
`Dboot`	is a list of `D`s (aligned list of transactions) that are generated from sampling with replacement on input samples (`mat`) `nboot` times.
`alpha`	is a significance threshold for hypothesis tests (Mann Whitney) that deploys for testing degrees of dependency, association direction, and causal direction. The default is 0.5.
`SignThs`	is a threshold for the degree of dependency for association direction inference. In the independence test of sign direction, to claim that any variables are dependent, the dependency degree must greater than this value significantly. The default is 0.05.
`CausalThs`	is a threshold for the degree of causal direction In the causal-direction test, to claim that any variables have causal relations, the degree of causal direction must greater than this value significantly. The default is 0.1.

Value

This function returns causal inference results from E1 matrix that is an output of bSCMdeConfoundingGraphFunc.

`Ehat`	An adjacency matrix of directed causal graph where `CausalGRes$Ehat[i,j]=1` implies i causes j.
`EValHat`	An adjacency matrix of weighted directed causal graph where edge weights are estimated means of probabilities of effect being 1 given cause being either 1 for positive association or 0 for negative association using CondProb() and bootstrapping to estimate.
`i`	An index
`j`	An index
`causalInfo$'i`, `j'$CDirConfValInv`	An `alpha`*100th percentile confidence interval of estimated conditional probability of effect j being 1/0 given cause i's value being either the same (positive association) or opposite (negative association).
`causalInfo$'i`, `j'$CDirConfInv`	An `alpha`*100th percentile confidence interval of estimated causal direction degree of i cause j.
`causalInfo$'i`, `j'$CDirmean`	A mean-estimated-causal-direction degree of i cause j.
`causalInfo$'i`, `j'$testRes2`	A Mann-Whitney hypothesis test result for existence of causal direction. The null hypothesis is that the distributions of causal-direction degrees of i,j differ by a location shift of `CausalThs` and the alternative is that distributions of causal-direction degrees of i,j is shifted greater than `CausalThs`.
`causalInfo$'i`, `j'$testRes1`	A Mann-Whitney hypothesis test result for existence of association by odd differences from `oddDiffFunc()`. The null hypothesis is that the distributions of absolute odd difference of i,j differ by a location shift of `IndpThs` and the alternative is that distributions of absolute odd difference of i,j is shifted greater than `IndpThs`.
`causalInfo$'i`, `j'$sign`	A direction of i,j association: 1 for positive, 0 for negative, and -1 for no association.
`causalInfo$'i`, `j'$SignConfInv`	An `alpha`*100th percentile confidence interval of i,j odd difference from bootstrapping.
`causalInfo$'i`, `j'$Signmean`	A mean of i,j odd difference from bootstrapping.

Examples

bSCMCausalGraphFunc(resC$ConfoundRes$E1,resC$depRes$Dboot)
bSCMCausalGraphFunc(resC$ConfoundRes$E1,resC$depRes$Dboot)

bSCMdeConfoundingGraphFunc function

Description

This function removes any association/dependency of variables i,j that have any confounding factor k s.t. given k, i and j are independent.

Usage

bSCMdeConfoundingGraphFunc(dat, IndpThs = 0.05, alpha = 0.05)
bSCMdeConfoundingGraphFunc(dat, IndpThs = 0.05, alpha = 0.05)

Arguments

`dat`	is the result of inferring dependencies between all pairs of variables from `bSCMDepndentGraphFunc()`.
`IndpThs`	is a threshold for the degree of dependency. In the independence test, to claim that any variables are dependent, the dependency degree must greater than this value significantly. The default is 0.05.
`alpha`	is a significance threshold for hypothesis tests (Mann Whitney) that deploys for testing degrees of dependency, association direction, and causal direction. The default is 0.5.

Value

This function returns an adjacency matrix of dependencies that have no confounding factors.

`E1`	An adjacency matrix of undirected graph after filtering associations without true causal directions from any confounding factor.
`E2`	A matrix of associations that have confounding factors where `E2[i,j]=0` if no confounding factor and `E2[i,j]=k` if k is a confounding factor of i and j.

Examples

bSCMdeConfoundingGraphFunc(resC$depRes)

bSCMdeConfoundingGraphFunc(resC$depRes)

bSCMDepndentGraphFastFunc function

Description

This function infers dependencies for all pairs of variables without bootstrapping.

Usage

bSCMDepndentGraphFastFunc(mat, IndpThs = 0.05)
bSCMDepndentGraphFastFunc(mat, IndpThs = 0.05)

Arguments

`mat`	is a matrix n by d where n is a number of transactions or samples and d is a number of dimensions.
`IndpThs`	is a threshold for the degree of dependency. In the independence test, to claim that any variables are dependent, the dependency degree must greater than this value significantly. The default is 0.05.

Value

This function returns results of dependency inference among variables.

`E0`	An adjacency matrix of undirected graph where there is an edge between any pair of variables if they are dependent.
`E0raw`	A matrix of the degree of dependency of variable pairs.

Examples

bSCMDepndentGraphFastFunc(mat)


bSCMDepndentGraphFastFunc(mat)

bSCMDepndentGraphFunc function

Description

This function infers dependencies for all pairs of variables with bootstrapping.

Usage

bSCMDepndentGraphFunc(
  mat,
  nboot = 100,
  alpha = 0.05,
  IndpThs = 0.05,
  pflag = FALSE
)
bSCMDepndentGraphFunc(
  mat,
  nboot = 100,
  alpha = 0.05,
  IndpThs = 0.05,
  pflag = FALSE
)

Arguments

`mat`	is a matrix n by d where n is a number of transactions or samples and d is a number of dimensions.
`nboot`	is a number of bootstrap replicates for bootstrapping deployed to infer confidence intervals and distributions for hypothesis tests. The default is 100.
`alpha`	is a significance threshold for hypothesis tests (Mann Whitney) that deploys for testing degrees of dependency, association direction, and causal direction. The default is 0.5.
`IndpThs`	is a threshold for the degree of dependency. In the independence test, to claim that any variables are dependent, the dependency degree must greater than this value significantly. The default is 0.05.
`pflag`	is a flag for printing progress message (TRUE). The default is FALSE (no printing).

Value

This function returns results of dependency inference among variables.

`E0`	An adjacency matrix of undirected graph where there is an edge between any pair of variables if they are dependent.
`E0pval`	A matrix of p-values from independence test of pairs of variables.
`E0mean`	A matrix of means of dependency degrees between variables.
`E0lowbound`	A matrix of lower bounds of dependency-degree confidence intervals between variables.
`depInfo$'i`, `j'$bmean`	A mean of dependency degrees between variables i and j.
`depInfo$'i`, `j'$confInv`	An `alpha`*100th percentile confidence interval of dependency degrees between variables i and j.
`depInfo$'i`, `j'$testRes`	A Mann-Whitney hypothesis test result for an independence test between variables i and j. The null hypothesis is that the distributions of dependency degrees of i,j differ by a location shift of `IndpThs` and the alternative is that distributions of dependency degrees of i,j is shifted greater than `IndpThs`.
`depInfo$'i`, `j'$indices`	A pair of indices of i and j in a numeric vector.
`Dboot`	A list of `D`s (aligned list of transactions) that are generated from sampling with replacement on input samples (`mat`) `nboot` times.

Examples

bSCMDepndentGraphFunc(mat, nboot=50)

bSCMDepndentGraphFunc(mat, nboot=50)

CausalGraphInferMainFunc function

Description

A framework to infer causality on binary data using techniques in frequent pattern mining and estimation statistics. Given a set of individual vectors S={x} where x(i) is a realization value of binary variable i, the framework infers empirical causal relations of binary variables i,j from S in a form of causal graph G=(V,E) where V is a set of nodes representing binary variables and there is an edge from i to j in E if the variable i causes j. The framework determines dependency among variables as well as analyzing confounding factors before deciding whether i causes j.

Note that all statistics (e.g. means) and confidence intervals as well as hypothesis testing are inferred by bootstrapping.

Usage

CausalGraphInferMainFunc(
  mat,
  alpha = 0.05,
  nboot = 100,
  IndpThs = 0.05,
  CausalThs = 0.1
)
CausalGraphInferMainFunc(
  mat,
  alpha = 0.05,
  nboot = 100,
  IndpThs = 0.05,
  CausalThs = 0.1
)

Arguments

`mat`	is a matrix n by d where n is a number of transactions or samples and d is a number of dimensions.
`alpha`	is a significance threshold for hypothesis tests (Mann Whitney) that deploys for testing degrees of dependency, association direction, and causal direction. The default is 0.5.
`nboot`	is a number of bootstrap replicates for bootstrapping deployed to infer confidence intervals and distributions for hypothesis tests. The default is 100.
`IndpThs`	is a threshold for the degree of dependency. In the independence test, to claim that any variables are dependent, the dependency degree must greater than this value significantly. The default is 0.05.
`CausalThs`	is a threshold for the degree of causal direction In the causal-direction test, to claim that any variables have causal relations, the degree of causal direction must greater than this value significantly. The default is 0.1.

Value

This function returns causal inference results. #TODO: provide list of results.

`depRes`	The result of inferring dependencies between all pairs of variables.
`ConfoundRes`	The result of filtering associations without true causal directions from any confounding factor.
`CausalGRes`	The result of inferring causal directions between all pairs of dependent variables that have no confounding factors.
`depRes$E0`	An adjacency matrix of undirected graph where there is an edge between any pair of variables if they are dependent.
`depRes$E0pval`	A matrix of p-values from independence test of pairs of variables.
`depRes$E0mean`	A matrix of means of dependency degrees between variables.
`depRes$E0lowbound`	A matrix of lower bounds of dependency-degree confidence intervals between variables.
`depRes$depInfo$'i`, `j'$bmean`	A mean of dependency degrees between variables i and j.
`depRes$depInfo$'i`, `j'$confInv`	An `alpha`*100th percentile confidence interval of dependency degrees between variables i and j.
`depRes$depInfo$'i`, `j'$testRes`	A Mann-Whitney hypothesis test result for an independence test between variables i and j. The null hypothesis is that the distributions of dependency degrees of i,j differ by a location shift of `IndpThs` and the alternative is that distributions of dependency degrees of i,j is shifted greater than `IndpThs`.
`depRes$depInfo$'i`, `j'$indices`	A pair of indices of i and j in a numeric vector.
`depRes$Dboot`	A list of `D`s (aligned list of transactions) that are generated from sampling with replacement on input samples (`mat`) `nboot` times.
`ConfoundRes$E1`	An adjacency matrix of undirected graph after filtering associations without true causal directions from any confounding factor.
`ConfoundRes$E2`	A matrix of associations that have confounding factors where `E2[i,j]=0` if no confounding factor and `E2[i,j]=k` if k is a confounding factor of i and j.
`CausalGRes$Ehat`	An adjacency matrix of directed causal graph where `CausalGRes$Ehat[i,j]=1` implies i causes j.
`CausalGRes$EValHat`	An adjacency matrix of weighted directed causal graph where edge weights are estimated means of probabilities of effect being 1 given cause being either 1 for positive association or 0 for negative association using CondProb() and bootstrapping to estimate
`CausalGRes$causalInfo$'i`, `j'$CDirConfValInv`	An `alpha`*100th percentile confidence interval of estimated conditional probability of effect j being 1/0 given cause i's value being either the same (positive association) or opposite (negative association).
`CausalGRes$causalInfo$'i`, `j'$CDirConfInv`	An `alpha`*100th percentile confidence interval of estimated causal direction degree of i cause j.
`CausalGRes$causalInfo$'i`, `j'$CDirmean`	A mean-estimated-causal-direction degree of i cause j.
`CausalGRes$causalInfo$'i`, `j'$testRes2`	A Mann-Whitney hypothesis test result for existence of causal direction. The null hypothesis is that the distributions of causal-direction degrees of i,j differ by a location shift of `CausalThs` and the alternative is that distributions of causal-direction degrees of i,j is shifted greater than `CausalThs`.
`CausalGRes$causalInfo$'i`, `j'$testRes1`	A Mann-Whitney hypothesis test result for existence of association by odd differences from `oddDiffFunc()`. The null hypothesis is that the distributions of absolute odd difference of i,j differ by a location shift of `IndpThs` and the alternative is that distributions of absolute odd difference of i,j is shifted greater than `IndpThs`.
`CausalGRes$causalInfo$'i`, `j'$sign`	A direction of i,j association: 1 for positive, 0 for negative, and -1 for no association.
`CausalGRes$causalInfo$'i`, `j'$SignConfInv`	An `alpha`*100th percentile confidence interval of i,j odd difference from bootstrapping.
`CausalGRes$causalInfo$'i`, `j'$Signmean`	A mean of i,j odd difference from bootstrapping.

Examples

resC<-CausalGraphInferMainFunc(mat = mat, nboot =50)

resC<-CausalGraphInferMainFunc(mat = mat, nboot =50)

comparePredAdjMatrix2TrueAdjMat

Description

comparePredAdjMatrix2TrueAdjMat is a support function that can compare two adjacency matrices: ground-truth and inferred matrices.

Usage

comparePredAdjMatrix2TrueAdjMat(trueAdjMat, adjMat)
comparePredAdjMatrix2TrueAdjMat(trueAdjMat, adjMat)

Arguments

`trueAdjMat`	a ground-truth matrix.
`adjMat`	an inferred matrix.

Value

This function returns a list of precision prec, recall rec, and F1 score F1 of inferred vs. groundtruth matrices.

Examples

# Generate simulation data
G<-matrix(FALSE,10,10) # groundtruth
G[1,c(4,7,8,10)]<-TRUE
G[2,c(5,7,9,10)]<-TRUE
G[3,c(6,8,9,10)]<-TRUE
comparePredAdjMatrix2TrueAdjMat(trueAdjMat=G,adjMat=G)

# Generate simulation data
G<-matrix(FALSE,10,10) # groundtruth
G[1,c(4,7,8,10)]<-TRUE
G[2,c(5,7,9,10)]<-TRUE
G[3,c(6,8,9,10)]<-TRUE
comparePredAdjMatrix2TrueAdjMat(trueAdjMat=G,adjMat=G)

CondProb function

Description

This function computes a confidence value of y given c or conf(y|z) from an aligned list D. For anyy[i],z[j], their values are -1 by default. The function computes the numbers of transactions that satisfy the following conditions.

All transactions must have values at any k position equal to z[k] for any z[k] that is not -1. Let count be the number of these transactions in D.
All transactions must have values at any k position equal to either z[k] or y[k] that is not -1. Let countTotal be the number of these transactions in D.

Usage

CondProb(D, y, z)
CondProb(D, y, z)

Arguments

`D`	is an aligned list of transactions that was converted from any matrix n by d `mat` using `D<-VecAlignment(mat)` where n is a number of transactions or samples and d is a number of dimensions for each sample.
`y`	is a d-dimensional vector.
`z`	is a d-dimensional vector.

Value

This function returns the ratio condP=count/countTotal, which is the confidence of y given z.

`condP`	The confidence of `y` given `z` in `D`.
`nD`	The subset of `D` such that all transactions have values at any position similar to `z[k]` when `z[k]` is not -1.
`count`	A number of transactions that have values at any position similar to either `z[k]` or `y[k]` that is not -1.
`countTotal`	A number of transactions in `nD`

Examples

d=10 # dimensions of example vectors
z<-numeric(d)-1
y<-numeric(d)-1
y[1]<-c(1)
z[c(2,3)]<-c(1,1)
CondProb(BiCausality::D,y=y,z=z)$condP # conf(inx1 is 1 |inx 2,3 are 1 ) y|z

d=10 # dimensions of example vectors
z<-numeric(d)-1
y<-numeric(d)-1
y[1]<-c(1)
z[c(2,3)]<-c(1,1)
CondProb(BiCausality::D,y=y,z=z)$condP # conf(inx1 is 1 |inx 2,3 are 1 ) y|z

confNetFunc function

Description

This function Computes a confidence network in data mining. Given a set of n transactions or samples in mat s.t. each transaction has d binary items. The conf(mat[,j]=1|mat[,i]=1) is a ratio of a number of samples in jth and ith dimensions that have values equal to one divided by a number of samples in the ith dimension that has a value equal to one. The confNetFunc computes the network where the nodes are dimensions and the edge weights are conf(mat[,j]=1|mat[,i]=1) for any directed edge from i to j.

Usage

confNetFunc(mat, ths = 0.1)
confNetFunc(mat, ths = 0.1)

Arguments

`mat`	is a matrix n by d where n is a number of transactions or samples and d is a number of dimensions.
`ths`	is a threshold parameter for cutting of the edge weights. There exists the directed edge from i to j if its edge weight if above or equal `ths`.

Value

This function returns a binary adjacency matrix confNet and the weighted adjacency matrix confValMat.

`confNet`	A binary adjacency matrix that has `confNet[i,j]=1` if `confValMat[i,j]>=ths`. Otherwise, it is zero.
`confValMat`	A weighted adjacency matrix where `confValMat[i,j]` is `conf(mat[,j]=1\|mat[,i]=1)`.

Examples

res<-confNetFunc(mat)

res<-confNetFunc(mat)

An example of aligned list of transactions

Description

A dataset containing simulated data that is used for examples in the package.

The D is an aligned list of transactions that was converted by using D<-VecAlignment(mat).

Usage

D
D

Format

An aligned list of a matrix with 200 samples and 10 dimensions generated from Bernoulli distribution.

D: It is an aligned list of transactions that was converted from mat.

getReachableNodes function

Description

getReachableNodes is a support function for inferring reachable nodes that have some directed path to a node targetNode. This function uses Breadth-first search (BFS) algorithm.

Usage

getReachableNodes(adjMat, targetNode)
getReachableNodes(adjMat, targetNode)

Arguments

`adjMat`	is an adjacency matrix of a directed graph of which its elements are binary: zero for no edge, and one for having an edge.
`targetNode`	is a node in a graph that we want to find a set of nodes that can reach this target node via some paths.

Value

This function returns a set of node IDs that have some directed path to a node targetNode.

Examples

# Given an example of adjacency matrix
A<-matrix(FALSE,5,5)
A[2,1]<-TRUE
A[c(3,4),2]<-TRUE
A[5,3]<-TRUE
# Get a set of reachable nodes of targetNode.

followers<-getReachableNodes(adjMat=A,targetNode=1)

# Given an example of adjacency matrix
A<-matrix(FALSE,5,5)
A[2,1]<-TRUE
A[c(3,4),2]<-TRUE
A[5,3]<-TRUE
# Get a set of reachable nodes of targetNode.

followers<-getReachableNodes(adjMat=A,targetNode=1)

getTransitiveClosureMat function

Description

getTransitiveClosureMat is a support function for inferring a transitive-closure adjacency matrix.

Usage

getTransitiveClosureMat(adjMat)
getTransitiveClosureMat(adjMat)

Arguments

adjMat

is an adjacency matrix of a directed graph of which its elements are binary: zero for no edge, and one for having an edge.

Value

This function returns a transitive-closure adjacency matrix.

Examples

# Given an example of adjacency matrix
A<-matrix(FALSE,5,5)
A[2,1]<-TRUE
A[c(3,4),2]<-TRUE
A[5,3]<-TRUE
# Get a set of reachable nodes of targetNode.

trsClosureMat<-getTransitiveClosureMat(adjMat=A)

# Given an example of adjacency matrix
A<-matrix(FALSE,5,5)
A[2,1]<-TRUE
A[c(3,4),2]<-TRUE
A[5,3]<-TRUE
# Get a set of reachable nodes of targetNode.

trsClosureMat<-getTransitiveClosureMat(adjMat=A)

indpFunc function

Description

This function computes the degree of dependency between variables. Let i and j be variables, if they are independent, then |p(i,j) -p(i)*p(j)| should be zero. Given the samples in the n by d matrix mat where n is a number of samples and d is a number of dimensions, an aligned list of transactions D is computed by D<-VecAlignment(mat).

Usage

indpFunc(D, i, j, z = c())
indpFunc(D, i, j, z = c())

Arguments

`D`	is an aligned list of transactions that was converted from `mat`.
`i`	is an ith dimension in `mat`.
`j`	is an jth dimension in `mat`.
`z`	is a conditioning d-dimensional vector on `D`. Given k non-negative-bit positions of `z`, all k bit positions of samples in the subset of `D` must have similar values with these bits.

Value

This function returns the degree of dependency between variables: zero implies both variables are independent, and non-zero value implies the degree of dependency (higher implies more dependent degree).

Examples

indpFunc(D,i=1,j=2)

indpFunc(D,i=1,j=2)

A simulation dataset

Description

A dataset containing simulated data that is used for examples in the package. The matrix mat is generated by the following code.

seedN<-2022

n<-200 # 200 individuals

d<-10 # 10 variables

mat<-matrix(nrow=n,ncol=d) # the input of framework

#Simulate binary data from Bernoulli distribution distribution where the probability of value being 1 is 0.5.

for(i in seq(n)) { set.seed(seedN+i)

mat[i,] <- rbinom(n=d, size=1, prob=0.5) }

mat[,1]<-mat[,2] | mat[,3] # 1 causes by 2 and 3

mat[,4] <-mat[,2] | mat[,5] # 4 causes by 2 and 5

mat[,6] <- mat[,1] | mat[,4] # 6 causes by 1 and 4

Usage

mat
mat

Format

A matrix with 200 samples and 10 dimensions generated from Bernoulli distribution.

mat: It is a 200 by 10 matrix where n is a number of transactions or samples and d is a number of dimensions.

...

num2Bits function

Description

Given a natural number and number of bits, the function provides an n-dimensional vector of bits that represents num. The ith bits of binary vector represents the ith bit of num. For example, if vec<-num2Bits(num=2,n=4), the first bit vec[1] is 0 and the second bit vec[2] is 1.

Usage

num2Bits(num, n = 32)
num2Bits(num, n = 32)

Arguments

`num`	is a natural number.
`n`	is a number of bits representing `num`.

Value

This function returns an n-dimensional vector of bits that represents num.

Examples

num2Bits(num=10,n=4)

num2Bits(num=10,n=4)

oddDiffFunc function

Description

Given the samples in the n by d matrix mat where n is a number of samples and d is a number of dimensions. This function computes an odd difference value of variables of ith and jth dimensions from a given an aligned list of transactions D (compute by D<-VecAlignment(mat)).

Usage

oddDiffFunc(D, i, j, z = c())
oddDiffFunc(D, i, j, z = c())

Arguments

`D`	is an aligned list of transactions that was converted from `mat`.
`i`	is an ith dimension in `mat` for computing the odd difference with.
`j`	is an jth dimension in `mat` for computing compute the odd difference with.
`z`	is a conditioning d-dimensional vector on `D`. Given k non-negative-bit positions of `z`, all k bit positions of samples in the subset of `D` must have similar values with these bits.

Value

This function returns an odd difference value of variables of ith and jth dimensions from D.

Examples

oddDiffFunc(D,i=1,j=2)

oddDiffFunc(D,i=1,j=2)

oddRatioFunc function

Description

Given the samples in the n by d matrix mat where n is a number of samples and d is a number of dimensions. This function computes an odd ratio value of variables of ith and jth dimensions from a given an aligned list of transactions D (compute by D<-VecAlignment(mat)).

Usage

oddRatioFunc(D, i, j, z = c(), slack = 0.001)
oddRatioFunc(D, i, j, z = c(), slack = 0.001)

Arguments

`D`	is an aligned list of transactions that was converted from `mat`.
`i`	is an ith dimension in `mat` for computing the odd ratio with.
`j`	is an jth dimension in `mat` for computing compute the odd ratio with.
`z`	is a conditioning d-dimensional vector on `D`. Given k non-negative-bit positions of `z`, all k bit positions of samples in the subset of `D` must have similar values with these bits.
`slack`	is a parameter to prevent the issue of division by zero.

Value

This function returns an odd ratio value of variables of ith and jth dimensions from D.

Examples

oddRatioFunc(D,i=1,j=2)

oddRatioFunc(D,i=1,j=2)

An example of causal inference result

Description

A dataset containing a result of causal inference from simulated data that is used for examples in the package.

Usage

resC
resC

Format

A result of causal inference using mat as an input.

resC: It is a result of causal inference using simData$mat as an input by running resC<-BiCausality::CausalGraphInferMainFunc(mat = mat,CausalThs=0.1, nboot =50, IndpThs=0.05).

supp function

Description

This function computes a support value from a matrix X given a values.

Usage

supp(X, values)
supp(X, values)

Arguments

`X`	is a matrix n by d where n is a number of transactions or samples and d is a number of dimensions for each sample.
`values`	is a d-dimensional vector we use to count how many of it within `X`.

Value

This function returns the support of values in X by counting the ratio of how many samples in X are similar to values

Examples

x <- rbinom(n=100, size=1, prob=0.5)
ny<-rbinom(n=100, size=1, prob=0.25)
y <- x |  ny
supp(X=cbind(x,y),values=c(1,1) )

x <- rbinom(n=100, size=1, prob=0.5)
ny<-rbinom(n=100, size=1, prob=0.25)
y <- x |  ny
supp(X=cbind(x,y),values=c(1,1) )

VecAlignment function

Description

This function rearranges the samples in the mat into an aligned list of transactions, which is mainly used by other functions in the package. Suppose mat[i,] is a binary vector we are interested, we use A<-bin2dec(mat[i,]) to store the decimal value of mat[i,] in A. Then, we call D[[A]]$count to get number of samples in mat that are similar to mat[i,] and the D[[A]]$name is mat[i,].

Usage

VecAlignment(mat)
VecAlignment(mat)

Arguments

mat

is a matrix n by d where n is a number of transactions or samples and d is a number of dimensions.

Value

This function returns an aligned list of transactions D, is an aligned list of transactions that was converted from any matrix n by d mat.

Examples

VecAlignment(mat=mat)

VecAlignment(mat=mat)

Package 'BiCausality'

Help Index

adjustmentProb function

Description

Usage

Arguments

Value

Examples

indpFunc function

Description

Usage

Arguments

Value

Examples

bin2dec function

Description

Usage

Arguments

Value

Examples

bIndpTest function

Description

Usage

Arguments

Value

Examples

bSCMCausalGraphFunc function

Description

Usage

Arguments

Value

Examples

bSCMdeConfoundingGraphFunc function

Description

Usage

Arguments

Value

Examples

bSCMDepndentGraphFastFunc function

Description

Usage

Arguments

Value

Examples

bSCMDepndentGraphFunc function

Description

Usage

Arguments

Value

Examples

CausalGraphInferMainFunc function

Description

Usage

Arguments

Value

Examples

comparePredAdjMatrix2TrueAdjMat

Description

Usage

Arguments

Value

Examples

CondProb function

Description

Usage

Arguments

Value

Examples

confNetFunc function

Description

Usage

Arguments

Value

Examples

An example of aligned list of transactions

Description

Usage

Format

getReachableNodes function

Description