constrained: Precision Matrix with Known Graph

In donaldRwilliams/GGMnonreg: Non-Regularized Gaussian Graphical Models

Description

Compute the maximum likelihood estimate of the precision matrix, given a known graphical structure (i.e., an adjacency matrix). This approach was originally described in "The Elements of Statistical Learning" \insertCite@see pg. 631, @hastie2009elementsGGMnonreg.

Usage

constrained(Sigma, adj)

Arguments

Sigma	Covariance matrix
adj	An adjacency matrix that encodes the constraints, where a zero indicates that element should be zero.

Value

A list containing the following:

• Theta: Inverse of the covariance matrix (precision matrix), that encodes the conditional (in)dependence structure.

• Sigma: Covariance matrix.

• wadj: Weighted adjacency matrix, corresponding to the partial correlation network.

Note

The algorithm is written in c++, and should scale to high dimensions.

Note there are a variety of algorithms for this purpose. Simulation studies indicated that this approach is both accurate and computationally efficient \insertCite@HFT therein, @emmert2019constrainedGGMnonreg

References

\insertAllCited

Examples

# data
Y <- ptsd

# estimate graph
fit <- ggm_inference(Y, boot = FALSE)

# constrain to zero
constrained_graph <- constrained(cor(Y), fit$adj)

donaldRwilliams/GGMnonreg documentation built on Nov. 13, 2021, 9:57 a.m.