CCI is an algorithm which discovers causation from observational data. More specifically, it is a constraint-based algorithm for causal discovery with cycles, latent variables and/or selection bias. Running CCI feels like running FCI, but CCI can handle cycles.
CCI discovers a partially oriented maximal almost ancestral graph (MAAG) of some directed graph G, provided that the global Markov property and d-separation faithfulness holds according to G. Such properties are reasonable when G is the directed graph of a structural equation model with independent errors and linearity holds, for example.
The academic article describing CCI in detail can be found here. Please cite the article if you use any of the code in this repository (Bibtex).
The package depends on the MASS and pcalg packages on CRAN, so please install these first. Then:
library(devtools)
install_github("ericstrobl/CCI")
library(CCI)
The algorithm essentially runs like pc() in the pcalg package. If you have your own data:
G=cci(suffStat, your_CItest, alpha=0.01, p=ncol(your_data))
where suffStat contains all the parameters/data needed for your conditional independence (CI) test of choice (your_CItest). The variable alpha is the type I error rate for the CI test. The variable p refers to the number of features in the dataset.
Here is a sample run with synthetic Gaussian data, where we set the CI test to be Fisher's z-test (gaussCItest):
a_DCG = generate_DCG_LE(20,2) #instantiate a directed cyclic graph with 20 vertices and on average 2 edges per node. Automatically includes 0-3 selection and 0-3 latent variables.
sample_DCG = sample_DCG_LE(nsamps=1000, a_DCG) #generate Gaussian samples from the DCG
suffStat=list(); suffStat$C = cor(sample_DCG); suffStat$n = 1000; # get all of the parameters needed by Fisher's z test
G=cci(suffStat,gaussCItest,alpha=0.01,p=ncol(sample_DCG)) # run CCI
G$maag #print the recovered partially oriented MAAG
The oracle outputs perfect conditional independence information, so CCI should make zero errors in this case. This means that each adjacency in the output should correspond to an inducing path and each endpoint should correctly capture the ancestral/non-ancestral relationship. You can call the oracle by setting the CI test to be dsepTest_fast; this function reads off the d-separation relations directly from the ground truth directed graph. Here is an example:
a_DCG = generate_DCG_LE(20,2) # generate a directed cyclic graph
suffStat = get_suffStat_oracle(a_DCG) # prepare all parameters for dsep oracle
plot(as(suffStat$graph,"graphNEL")) # plot the ground truth directed graph
G <- cci(suffStat, indepTest=dsepTest_fast, alpha = 0.01, p=length(suffStat$actual_indices)); # run cci
rownames(G$maag)=suffStat$actual_indices; #re-number the indices of the partially oriented MAAG so that they correspond to the numberings in the directed cyclic graph
colnames(G$maag)=suffStat$actual_indices;
G$maag
Let S denote the selection variables
G$maag[i,j] = 0 means that an inducing path does not exist between between i and j
G$maag[i,j] != 0 (not equal to 0) means there exists an inducing path between i and j
G$maag[i,j] = 1 means CCI does not know if j is an ancestor or not an ancestor of i or S
G$maag[i,j] = 2 means j is not an ancestor of i or S
G$maag[i,j] = 3 means j is an ancestor of i or S