constrained {IRCcheck}

Constrained Precision Matrix

Description

Compute the maximum likelihood estimate, given certain elements are constrained to zero (e.g., an adjacency matrix). This approach is described in Hastie et al. (2009).

Usage

constrained(Sigma, adj)

Arguments

Sigma

Covariance matrix

adj

Matrix with constraints. A zero indicates that element should be constrained to zero.

Value

A list containing the inverse covariance matrix and the covariance matrix.

Note

The algorithm is written in c++.

References

Hastie T, Tibshirani R, Friedman J (2009). The elements of statistical learning: data mining, inference, and prediction. Springer Science \& Business Media.

Examples

# random adj 
# 90 % sparsity (roughly)
p <- 20
adj <- matrix(sample(0:1, size = p^2, replace = TRUE, 
              prob = c(0.9, 0.1) ), 
              nrow = p, ncol = p)

adj <-  symm_mat(adj)

diag(adj) <- 1

# random correlation matrix
set.seed(1)
cors <- cov2cor(
  solve(
  rWishart(1, p + 2, diag(p))[,,1])
)

# constrain to zero
net <- constrained(cors, adj = adj)