CAM (version 1.0)

CAM: Causal Additive Model

Description

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

Usage

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)

Arguments

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.

Value

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

Details

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.

References

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.

Examples

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)