Package '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)

---

L1 Regularized Logistic Regression

Description

L1 Regularized logistic regression using OWL-QN L-BFGS-B optimization.

Usage

logreg(X, y, nlambda = 50, lambda.min.ratio = 0.001, lambda = NULL,
  scale = TRUE, type = 2)

Arguments

X	The design matrix.
y	Vector of binary observations of length equal to nrow(X).
nlambda	(positive integer) The number of parameters in the regularization path (default 50).
lambda.min.ratio	(non-negative double) The ratio of max(lambda) / min(lambda) (default 1e-3).
lambda	A user-supplied vector of regularization parameters. Under the default option (NULL), the function computes a regularization path using the input data.
scale	(boolean) Whether to scale X before running the regression. The output parameters will always be rescaled. Use FALSE if X is already scaled.
type	(integer 1 or 2) Type 1 aggregates the input data based on repeated rows in X. Type 2 (default) uses the data as is, and is generally faster. Use Type 1 if the data contains several repeated rows.

Value

A list containing the matrix of fitted weights (wmat), the vector of regularization parameters, sorted in decreasing order (lambda), and the vector of log-likelihoods corresponding to lambda (logliks).

Examples

# simulate some linear regression data
n <- 1e3
p <- 100
X <- matrix(rnorm(n*p),n,p)
wt <- sample(seq(0,9),p+1,replace = TRUE) / 10
z <- cbind(1,X) %*% wt + rnorm(n)
probs <- 1 / (1 + exp(-z))
y <- sapply(probs, function(p) rbinom(1,1,p))

m1 <- logreg(X, y)
m2 <- logreg(X, y, nlambda = 100, lambda.min.ratio = 1e-4, type = 1)

## Not run: 
# Performance comparison
library(glmnet)
library(microbenchmark)
nlambda = 50; lambda.min.ratio = 1e-3
microbenchmark(
  logreg_type1 = logreg(X, y, nlambda = nlambda,
                         lambda.min.ratio = lambda.min.ratio, type = 1),
  logreg_type2 = logreg(X, y, nlambda = nlambda,
                         lambda.min.ratio = lambda.min.ratio, type = 2),
  glmnet       = glmnet(X, y, family = "binomial",
                         nlambda = nlambda, lambda.min.ratio = lambda.min.ratio),
  times = 20L
)

## End(Not run)

---

rIsing: High-Dimensional Ising Model Selection.

Description

Fits an Ising model to a binary dataset using L1-regularized logistic regression and BIC. Also includes a fast lasso logistic regression function for high-dimensional problems. Uses the 'libLBFGS' optimization library by Naoki Okazaki.

rIsing functions

• logreg: L1-regularized logistic regression using OWL-QN L-BFGS-B optimization.

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

---