LINGAM function

Linear non-Gaussian Acyclic Models (LiNGAM)

Fits a Linear non-Gaussian Acyclic Model (LiNGAM) to the data and returns the corresponding DAG.

For details, see the reference below.

lingam(X, verbose = FALSE)

## For back-compatibility; this is *deprecated*
LINGAM(X, verbose = FALSE)

Arguments

• X: n x p data matrix (n: sample size, p: number of variables).
• verbose: logical or integer indicating that increased diagnostic output is to be provided.

Returns

lingam() returns an object of (S3) class "LINGAM", basically a list with components - Bpruned: a $p x p$ matrix $B$ of linear coefficients, where $B_{i,j}$ corresponds to a directed edge from $j$ to $i$.

• stde: a vector of length $p$ with the standard deviations of the estimated residuals

• ci: a vector of length $p$ with the intercepts of each equation

  ...``...``...``...``...``...

LINGAM() --- deprecated now --- returns a list with components - Adj: a $p x p$ 0/1 adjacency matrix $A$. A[i,j] == 1 corresponds to a directed edge from i to j.

• B: $p x p$ matrix of corresponding linear coefficients. Note it corresponds to the transpose of Adj, i.e., identical( Adj, t(B) != 0 ) is true.

References

S. Shimizu, P.O. Hoyer, A. Hyv"arinen, A. Kerminen (2006) A Linear Non-Gaussian Acyclic Model for Causal Discovery; Journal of Machine Learning Research 7 , 2003--2030.

Author(s)

Of LINGAM() and the underlying functionality,

Patrik Hoyer patrik.hoyer@helsinki.fi, Doris Entner entnerd@hotmail.com, Antti Hyttinen antti.hyttinen@cs.helsinki.fi and Jonas Peters jonas.peters@tuebingen.mpg.de.

See Also

fastICA from package fastICA is used.

Examples

##################################################
## Exp 1
##################################################
set.seed(1234)
n <- 500
eps1 <- sign(rnorm(n)) * sqrt(abs(rnorm(n)))
eps2 <- runif(n) - 0.5

x2 <- 3 + eps2
x1 <- 0.9*x2 + 7 + eps1

#truth: x1 <- x2
trueDAG <- cbind(c(0,1),c(0,0))

X <- cbind(x1,x2)
res <- lingam(X)

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

cat("estimated DAG:\n")
as(res, "amat")

cat("\n true constants:\n")
show(c(7,3))
cat("estimated constants:\n")
show(res$ci)

cat("\n true (sample) noise standard deviations:\n")
show(c(sd(eps1), sd(eps2)))
cat("estimated noise standard deviations:\n")
show(res$stde)

##################################################
## Exp 2
##################################################
set.seed(123)
n <- 500
eps1 <- sign(rnorm(n)) * sqrt(abs(rnorm(n)))
eps2 <- runif(n) - 0.5
eps3 <- sign(rnorm(n)) * abs(rnorm(n))^(1/3)
eps4 <- rnorm(n)^2

x2 <-                eps2
x1 <-   0.9*x2     + eps1
x3 <-   0.8*x2     + eps3
x4 <- -x1  -0.9*x3 + eps4

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

trueDAG <- cbind(x1 = c(0,1,0,0),
                 x2 = c(0,0,0,0),
                 x3 = c(0,1,0,0),
                 x4 = 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

res1 <- lingam(X, verbose = TRUE)# details on LINGAM
res2 <- lingam(X, verbose = 2)   # details on LINGAM and fastICA
## results are the same, of course:
stopifnot(identical(res1, res2))
cat("true DAG:\n")
show(trueDAG)

cat("estimated DAG:\n")
as(res1, "amat")