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Groupwise Block-Diagonal Sparsifier

Source: R/sparsify_block_diag.R
sparsify_block_diag.Rd

Make a precision-like matrix block-diagonal according to group membership, keeping only within-group blocks. Optionally, further reduce selected within-group blocks to diagonal-only (identity-like) structure.

Usage

sparsify_block_diag(mat, membership, group.diag = NULL)

Arguments

mat

A p-by-p precision-like matrix specifying the base matrix to be masked.

membership

An integer vector specifying the group membership. The length of membership must be consistent with the dimension p.

group.diag

(default = NULL)

  1. NULL: Make mat block-diagonal, i.e., only keep all within-group blocks.

  2. An integer vector specifying which within-group blocks are further reduced to diagonal-only structure (based on the block-diagonal form).

Value

A list containing:

Omega

The masked precision matrix.

Sigma

The covariance matrix, i.e., the inverse of Omega.

sparsity

Proportion of zero entries in Omega.

membership

An integer vector specifying the group membership.

Examples

## reproducibility for everything
set.seed(1234)

## precision matrix estimation
X <- matrix(rnorm(200), 10, 20)
membership <- c(rep(1,5), rep(2,5), rep(3,4), rep(4,6))
est <- grasps(X, membership = membership, penalty = "lasso", crit = "BIC")

## block-diagonalizel; within-group block for group 3 made diagonal-only.
res <- sparsify_block_diag(est$hatOmega, membership, group.diag = 3)

## visualization
visualize(res$Omega, res$membership)