CAM: Causal Additive Model
In CAM: Causal Additive Model (CAM)

Description Usage Arguments Details Value Author(s) References Examples

fits a causal additive model using the CAM algorithm, see references below

CAM(X, scoreName = "SEMGAM", parsScore = list(numBasisFcts = 10), numCores = 1, 
    maxNumParents = min(dim(X)[2] - 1, round(dim(X)[1]/20)), output = FALSE, 
    variableSel = FALSE, variableSelMethod = selGamBoost, 
    variableSelMethodPars = list(atLeastThatMuchSelected = 0.02, 
    atMostThatManyNeighbors = 10), pruning = FALSE, pruneMethod = selGam, 
    pruneMethodPars = list(cutOffPVal = 0.001, numBasisFcts = 10), intervData = FALSE, 
    intervMat = NA)

`X`	nxp matrix of training inputs (n data points, p dimensions)
`scoreName`	specifies the model type which is used to compute the score. Default is "SEMGAM" which assumes a generalized additive model class. Other options include "SEMLIN" which fits a linear model.
`parsScore`	additional parameters can be supported to the score function.
`numCores`	specifies the number of cores that can be used for computation.
`maxNumParents`	specifies the maximal number of parents that are allowed in the model.
`output`	shall output be printed to the console (TRUE/FALSE)
`variableSel`	specifies whether initial variable selection (Step 1 of CAM algorithm) shall be performed (TRUE) or not (FALSE). Initial variable selection reduces the number of possible parents for a given node and therefore enables computing the causal structure for large p.
`variableSelMethod`	specifies the method that is used for variable selection. Default is selGamBoost which uses the gamboost function from mboost package. Other options include: selGam (gam() from mgcv), selLm based on linear regression, selLasso based on Lasso regression from package glmnet.
`variableSelMethodPars`	optional parameters to modify settings of the selection method.
`pruning`	specifies whether pruning (Step 3 of CAM algorithm) shall be performed (TRUE) or not (FALSE). Pruning reduces the number of edges in the estimated causal structure.
`pruneMethod`	specifies the method used for the pruning step. Default is selGAM which is based on the gam() function from the mgcv package.
`pruneMethodPars`	optional parameters to tune the pruning step.
`intervData`	boolean that indicates whether we use interventional data.
`intervMat`	the matrix intervMat has the same dimension as X. entry (i,j) == TRUE indicates that in experiment i, variable j has been intervened on.

The code fits a CAM model. See the references below for more details. Identifiability results for the model class can be found in

J. Peters, J. Mooij, D. Janzing, B. Sch\"olkopf: Causal Discovery with Continuous Additive Noise Models, JMLR 15:2009-2053, 2014.

list of attributes of the final estimated causal structure

`Adj`	adjacency matrix of estimated causal graph
`Score`	Total edge score of estimated graph
`timesVec`	Vector containing various time measurements for execution times of the individual steps of the CAM algorithm

Jonas Peters <jonas.peters@tuebingen.mpg.de> and Jan Ernest <ernest@stat.math.ethz.ch>

P. B\"uhlmann, J. Peters, J. Ernest: CAM: Causal Additive Models, high-dimensional Order Search and Penalized Regression Annals of Statistics 42:2526-2556, 2014.

n <- 500
eps1<-rnorm(n)
eps2<-rnorm(n)
eps3<-rnorm(n)
eps4<-rnorm(n)

x2 <- 0.5*eps2
x1 <- 0.9*sign(x2)*(abs(x2)^(0.5))+0.5*eps1
x3 <- 0.8*x2^2+0.5*eps3
x4 <- -0.9*sin(x3) - abs(x1) + 0.5*eps4

X <- cbind(x1,x2,x3,x4)

trueDAG <- cbind(c(0,1,0,0),c(0,0,0,0),c(0,1,0,0),c(1,0,1,0))
## x4 <- x3 <- x2 -> x1 -> x4
## adjacency matrix:
## 0 0 0 1
## 1 0 1 0
## 0 0 0 1
## 0 0 0 0

estDAG <- CAM(X, scoreName = "SEMGAM", numCores = 1, output = TRUE, variableSel = FALSE, 
              pruning = TRUE, pruneMethod = selGam, pruneMethodPars = list(cutOffPVal = 0.001))

cat("true DAG:\n")
show(trueDAG)

cat("estimated DAG:\n")
show(estDAG$Adj)

Loading required package: glmnet
Loading required package: Matrix
Loading required package: foreach
Loaded glmnet 2.0-16

Loading required package: mboost
Loading required package: parallel
Loading required package: stabs
This is mboost 2.9-1. See 'package?mboost' and 'news(package  = "mboost")'
for a complete list of changes.

Loading required package: mgcv
Loading required package: nlme
This is mgcv 1.8-28. For overview type 'help("mgcv-package")'.
number of cores: 1 

 compute score entry for regressing 1 on 1                   

 compute score entry for regressing 1 on 2                   

 compute score entry for regressing 1 on 3                   

 compute score entry for regressing 1 on 4                   

 compute score entry for regressing 2 on 1                   

 compute score entry for regressing 2 on 2                   

 compute score entry for regressing 2 on 3                   

 compute score entry for regressing 2 on 4                   

 compute score entry for regressing 3 on 1                   

 compute score entry for regressing 3 on 2                   

 compute score entry for regressing 3 on 3                   

 compute score entry for regressing 3 on 4                   

 compute score entry for regressing 4 on 1                   

 compute score entry for regressing 4 on 2                   

 compute score entry for regressing 4 on 3                   

 compute score entry for regressing 4 on 4                   
Object size of computeScoreMatTmp:  1040 

 Included edge (from, to)  2 1 

 compute score entry for regressing 1 on 2 3                   

 compute score entry for regressing 1 on 2 4                   
 Included edge (from, to)  3 4 

 compute score entry for regressing 4 on 3 1                   

 compute score entry for regressing 4 on 3 2                   
 Included edge (from, to)  1 4 

 compute score entry for regressing 4 on 1 3 2                   
 Included edge (from, to)  2 3 

 compute score entry for regressing 3 on 2 1                   
 Included edge (from, to)  1 3 

 Included edge (from, to)  2 4 

 Performing pruning ... 
 pruning variable: 1 
considered parents: 2 
vector of p-values: 3.842128e-93 
pruning variable: 2 
considered parents:  
pruning variable: 3 
considered parents: 1 2 
vector of p-values: 0.5745814 5.963104e-24 
pruning variable: 4 
considered parents: 1 2 3 
vector of p-values: 4.4215e-50 0.5727815 4.526757e-70 
amount of time for variable selection: 0 
amount of time computing the initial scoreMat: 0.311 
amount of time checking for cycles: 0 
amount of time computing updates for the scoreMat: 0.194 , doing 6 updates.
amount of time for pruning: 0.091 
amount of time for finding maximum: 0 
amount of time in total: 0.596 
true DAG:
     [,1] [,2] [,3] [,4]
[1,]    0    0    0    1
[2,]    1    0    1    0
[3,]    0    0    0    1
[4,]    0    0    0    0
estimated DAG:
     [,1] [,2] [,3] [,4]
[1,]    0    0    0    1
[2,]    1    0    1    0
[3,]    0    0    0    1
[4,]    0    0    0    0