sparsify_block_banded: Groupwise Block-Banded Sparsifier

In grasps: Groupwise Regularized Adaptive Sparse Precision Solution

Groupwise Block-Banded Sparsifier

Description

Make a precision-like matrix block-banded according to group membership, keeping only entries within specified group neighborhoods.

Usage

sparsify_block_banded(mat, membership, neighbor.range = 1)

Arguments

mat	A d \times d 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 d.
neighbor.range	An integer (default = 1) specifying the neighbor range, where groups whose labels differ by at most neighbor.range are considered neighbors and kept in the mask.

Value

An object with S3 class "sparsify_block_banded" containing the following components:

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

library(grasps)

## 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")

## default: keep blocks within ±1 of each group
res1 <- sparsify_block_banded(est$hatOmega, membership, neighbor.range = 1)
plot(res1)

## wider band: keep blocks within ±2 of each group
res2 <- sparsify_block_banded(est$hatOmega, membership, neighbor.range = 2)
plot(res2)

## special case: block-diagonal matrix
res3 <- sparsify_block_banded(est$hatOmega, membership, neighbor.range = 0)
plot(res3)

grasps documentation built on Nov. 28, 2025, 1:06 a.m.