fciPlus: Estimate a PAG by the FCI+ Algorithm

Description

Estimate a Partial Ancestral Graph (PAG) from observational data, using the FCI+ (Fast Causal Inference) Algorithm.

Usage

fciPlus(suffStat, indepTest, alpha, labels, p, verbose=TRUE)

Arguments

suffStat

sufficient statistics: A named list containing all necessary elements for the conditional independence decisions in the function indepTest.

indepTest

a function for testing conditional independence. The function is internally called as indepTest(x,y, S, suffStat), and tests conditional independence of x and y given S. Here, x and y are variables, and S is a (possibly empty) vector of variables (all variables are denoted by their column numbers in the adjacency matrix). suffStat is a list with all relevant information, see above. The return value of indepTest() is the p-value of the test for conditional independence.

alpha

numeric significance level (in $(0, 1)$) for the individual conditional independence tests.

labels

(optional) character vector of variable (or “node”) names. Typically preferred to specifying p.

(optional) number of variables (or nodes). May be specified if labels are not, in which case labels is set to 1:p.

verbose

logical indicating if progress of the algorithm should be printed. The default is true, which used to be hard coded previously.

Value

An object of class fciAlgo (see fciAlgo) containing the estimated graph (in the form of an adjacency matrix with various possible edge marks), the conditioning sets that lead to edge removals (sepset) and several other parameters.

Details

A variation of FCI (Fast Causal Inference). For details, please see the references, and also fci.

References

T. Claassen, J. Mooij, and T. Heskes (2013). Learning Sparse Causal Models is not NP-hard. In UAI 2013, Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence

Examples

Run this code

##################################################
## Example without latent variables
##################################################

## generate a random DAG ( p = 7 )
set.seed(42)
p <- 7
myDAG <- randomDAG(p, prob = 0.4)

## find PAG using the FCI+ algorithm on "Oracle"
suffStat <- list(C = cov2cor(trueCov(myDAG)), n = 10^9)
m.fci <- fciPlus(suffStat, indepTest=gaussCItest,
                 alpha = 0.9999, p=p)
summary(m.fci)

## require("Rgraphviz")
sfsmisc::mult.fig(2, main="True DAG  //  fciPlus(.) \"oracle\" estimate")
plot(myDAG)
plot(m.fci)

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