ising {rIsing}

High-Dimensional Ising Model Selection

Description

Ising Model selection using L1-regularized logistic regression and extended BIC.

Usage

ising(X, gamma = 0.5, min_sd = 0, nlambda = 50,
  lambda.min.ratio = 0.001, symmetrize = "mean")

Arguments

X

The design matrix.

gamma

(non-negative double) Parameter for the extended BIC (default 0.5). Higher gamma encourages sparsity. See references for more details.

min_sd

(non-negative double) Columns of X with standard deviation less than this value will be excluded from the graph.

nlambda

(positive integer) The number of parameters in the regularization path (default 50). A longer regularization path will likely yield more accurate results, but will take more time to run.

lambda.min.ratio

(non-negative double) The ratio min(lambda) / max(lambda) (default 1e-3).

symmetrize

The method used to symmetrize the output adjacency matrix. Must be one of "min", "max", "mean" (default), or FALSE. "min" and "max" correspond to the Wainwright min/max, respectively (see reference 1). "mean" corresponds to the coefficient-wise mean of the output adjacency matrix and its transpose. If FALSE, the output matrix is not symmetrized.

Value

A list containing the estimated adjacency matrix (Theta) and the optimal regularization parameter for each node (lambda), as selected by extended BIC.

References

1. Ravikumar, P., Wainwright, M. J. and Lafferty, J. D. (2010). High-dimensional Ising model selection using L1-regularized logistic regression. https://arxiv.org/pdf/1010.0311v1

2. Barber, R.F., Drton, M. (2015). High-dimensional Ising model selection with Bayesian information criteria. https://arxiv.org/pdf/1403.3374v2

Examples

## Not run: 
# simulate a dataset using IsingSampler
library(IsingSampler)
n = 1e3
p = 10
Theta <- matrix(sample(c(-0.5,0,0.5), replace = TRUE, size = p*p), nrow = p, ncol = p)
Theta <- Theta + t(Theta) # adjacency matrix must be symmetric
diag(Theta) <- 0
X <- unname(as.matrix(IsingSampler(n, graph = Theta, thresholds = 0, method = "direct") ))
m1 <- ising(X, symmetrize = "mean", gamma = 0.5, nlambda = 50)

# Visualize output using igraph
library(igraph)
ig <- graph_from_adjacency_matrix(m1$Theta, "undirected", weighted = TRUE, diag = FALSE)
plot.igraph(ig, vertex.color = "skyblue")

## End(Not run)