graph_from_top: Find graph from topological ordering
In Laksafoss/CausDiscEqVar: Causal Discovery with Equal Variance Assumption

Description Usage Arguments Details Value See Also Examples

Given data and a topological ordering of the causal graph this function will estimate the causal graph itself.

1	graph_from_top(X, top, measure = "deviance", which = "1se")

`X`	A matrix containing the observed variables
`top`	A topological ordering of the variables
`measure`	Either "mse", "mae"
`which`	Either "min" or "1se"

To estimate the graph, the parents of each variable is fund via model selection. As the underlying grap is assumed to be a DAG the parents of a variable X_{(j)} must be found among the variables with a lower ordering (X_{(i)})_{i<j}.

All model selection is done via cross-validation lasso.

the coefficient graph estimated from the data. This is a graph which has values different from zero iff there is an arrow in the estimated causal graph. The values of the non-zero entries in this matrix are the estimated (causal) effects.

The wrapper function graph_est combines the function top_order, which estimates the topological ordering of the causal graph from data, and graph_from_top into one function that estimates the causal graph from the data.

# we create some data from the graph B
n <- 1000
B <- matrix(c(0,1,0,1,
              0,0,2,0,
              0,0,0,1,
              0,0,0,0), ncol = 4, nrow = 4, byrow = TRUE)
X <- matrix(0, ncol = 4, nrow = n)
for (i in 1:4) {
  X[ ,i] <- X %*% B[ ,i] + rnorm(n)
}

# we then find the graph using a topological ordering
top <- c(1,2,3,4) # from B we know this to be the true ordering
graph_from_top(X, top)