spacejam (version 1.1)

spacejam-package: Fit sparse conditional independence graphs with joint additive models

Description

This package is called `spacejam', which can be thought to stand for SParse Conditional Estimation with Joint Additive Models. The two main functions of this package, SJ and SJ.dag, estimate conditional independence graphs and DAGs using flexible node-wise regressions, employing a standardized group lasso to encourage sparsity. Details of the method are given in Voorman, Shojaie and Witten (2013). Graph Estimation with Joint Additive Models.

Details

Package:

spacejam

Type:

Package

Version:

1.1

Date:

2013-04-08

License:

GPL >= 2

The package includes the following functions:

SJ and SJ.dag:

Estimate the conditional independence graph, or directed acyclic graph, based on observed data

rdag:

construct a random directed acyclic graph

moralize:

Determine the moral graph, which is the conditional independence graph associated with the directed graph

generate.dag.data:

Generate data from a bayesian network

plot.SJ:

Plot SJ and SJ.dag objects.

References

Voorman, Shojaie and Witten (2013). Graph Estimation with Joint Additive Models. Submitted to Biometrika. available on ArXiv or from authors upon request

See Also

spacejam SJ generate.dag.data

Examples

#########Create graph and distribution used in Figure 2 of Voorman, Shojaie and Witten (2013):
p <- 100 #variables
n <- 50 #observations

#Generate Graph
set.seed(20)
g <- rdag(p,80)
mylayout <- layout.fruchterman.reingold(g)

par(mfrow=c(1,2))
plot(g, layout = mylayout, edge.color = "gray50", 
        vertex.color = "red", vertex.size = 3, vertex.label = NA, 
        edge.arrow.size = 0.4)
plot(moralize(g), layout = mylayout, edge.color = "gray50", 
        vertex.color = "red", vertex.size = 3, vertex.label = NA, 
        edge.arrow.size = 0.4)

#create a distribution on the DAG using cubic polynomials with random normal coefficients 
#with standard deviations of 1, 0.5 and 0.5, (i.e. giving more weight to linear association than quadratic or cubic)
data <- generate.dag.data(g,n,basesd=c(1,0.5,0.5))
X <- data$X

#Fit conditional independence graph at one lambda 
fit1 <- SJ(X, lambda = 0.6)

#Fit conditional independence graph at 10 (hopefully reasonable) lambdas:
fit2 <- SJ(X, length = 10)

#Fit conditional independence graph using quadratic basis functions:
fit3 <- SJ(X, bfun = function(x){cbind(x,x^2)}, length = 10)

#Fit the DAG using default causal ordering 1:p, and at 10 lambdas
fit4 <- SJ.dag(X, length = 10)
fit4

#plot the DAGs, and the true graph
par(mfrow=c(1,3))
plot(g, layout=mylayout, edge.color = "gray50", vertex.color = "red", vertex.size = 3, vertex.label = NA, edge.arrow.size = 0.4, main="True DAG")
plot(fit4, layout = mylayout, which= 4, main= paste0("lambda = ",round(fit4$lambda[4],2) ))
plot(fit4, layout = mylayout, main = "min BIC")

###For additional replications using the same DAG distribution use e.g.
data <- generate.dag.data(g,n,funclist = data$funclist)


#### Screen out edges whose corresponding nodes have low spearman correlation:
# useful for approximating spacejam in high dimesnions
S <- cor(data$X, method = "spearman")
G.max <- S > 0.1
mean(G.max) #~75% of edges removed

system.time({fit.screen <- SJ(X, G.max = G.max,length=20)})
system.time({fit.noscreen <- SJ(X,length = 20)})

plot(fit.screen, layout=mylayout)
plot(fit.noscreen, layout=mylayout)