Groupwise Regularized Adaptive Sparse Precision Solution.

grasps

Groupwise Regularized Adaptive Sparse Precision Solution

The goal of grasps is to provide a collection of statistical methods that incorporate both element-wise and group-wise penalties to estimate a precision matrix, making them user-friendly and useful for researchers and practitioners.

$$ \hat{\Omega}(\lambda,\alpha,\gamma) = {\arg\min}{\Omega \succ 0} { -\log\det(\Omega) + \text{tr}(S\Omega) + \mathcal{P}{\lambda,\alpha,\gamma}(\Omega) }, $$ $$ \mathcal{P}{\lambda,\alpha,\gamma}(\Omega) = \alpha \mathcal{P}^\text{idv}{\lambda,\gamma}(\Omega) + (1-\alpha) \mathcal{P}^\text{grp}{\lambda,\gamma}(\Omega), $$ $$ \mathcal{P}^\text{idv}{\lambda,\gamma}(\Omega) = \sum_{i,j} P_{\lambda,\gamma}(\lvert\omega_{ij}\rvert), $$ $$ \mathcal{P}^\text{grp}{\lambda,\gamma}(\Omega) = \sum{g,g^\prime} P_{\lambda,\gamma}(\lVert\Omega_{gg^\prime}\rVert_F). $$

For more details, see the vignette Penalized Precision Matrix Estimation in grasps.

Penalties

The package grasps provides functions to estimate precision matrices using the following penalties:

See the vignette Penalized Precision Matrix Estimation in grasps for more details.

Installation

• You can install the released version of grasps from CRAN with:

install.packages("grasps")

• You can install the development version of grasps from GitHub with:

# install.packages("pak")
pak::pkg_install("Carol-seven/grasps")

Example

library(grasps)

## reproducibility for everything
set.seed(1234)

## block-structured precision matrix based on SBM
sim <- gen_prec_sbm(p = 30, K = 3,
                    within.prob = 0.25, between.prob = 0.05,
                    weight.dists = list("gamma", "unif"),
                    weight.paras = list(c(shape = 20, rate = 10),
                                        c(min = 0, max = 5)),
                    cond.target = 100)
## ground truth visualization
plot(sim)

## n-by-p data matrix
library(MASS)
X <- mvrnorm(n = 20, mu = rep(0, 30), Sigma = sim$Sigma)

## precision matrix: adaptive lasso; BIC
prec <- grasps(X = X, membership = sim$membership, penalty = "adapt", crit = "BIC")

## precision matrix visualization
plot(prec)

## performance
performance(hatOmega = prec$hatOmega, Omega = sim$Omega)
#>      measure    value
#> 1   sparsity   0.8805
#> 2  Frobenius  23.9013
#> 3         KL   7.6775
#> 4  quadratic  69.1639
#> 5   spectral  12.3571
#> 6         TP  23.0000
#> 7         TN 358.0000
#> 8         FP  29.0000
#> 9         FN  25.0000
#> 10       TPR   0.4792
#> 11       FPR   0.0749
#> 12        F1   0.4600
#> 13       MCC   0.3904

## adjacency matrix: diagonal = 0; raw partial correlations;
##                   no thresholding; weighted network
adj <- prec_to_adj(prec$hatOmega,
                   diag.zero = TRUE, absolute = FALSE,
                   threshold = NULL, weighted = TRUE)

## adjacency matrix visualization
plot(adj)

Reference