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.

$$\hat{\Omega}(\lambda,\alpha,\gamma) = {\arg\min}{\Omega \succ 0} { -\log\det(\Omega) + \text{tr}(S\Omega) + \lambda P{\alpha,\gamma}(\Omega) },$$

$$P_{\alpha,\gamma}(\Omega) = \alpha P^\text{idv}\gamma(\Omega) + (1-\alpha) P^\text{grp}\gamma(\Omega),$$

$$P^\text{idv}\gamma(\Omega) = \sum{i,j} p_\gamma(\vert\omega_{ij}\vert),$$

$$P^\text{grp}\gamma(\Omega) = \sum{g,g^\prime} p_\gamma(\Vert\Omega_{gg^\prime}\Vert_F).$$

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 development version of grasps from GitHub with:

# install.packages("devtools")
devtools::install_github("Carol-seven/grasps")

Example

library(grasps)

## reproducibility for everything
set.seed(1234)

## block-structured precision matrix based on SBM
sim <- gen_prec_sbm(d = 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)

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

## solution
res <- grasps(X = X, membership = sim$membership, penalty = "adapt", crit = "HBIC")

## visualization
plot(res)

## performance
performance(hatOmega = res$hatOmega, Omega = sim$Omega)
#>      measure    value
#> 1   sparsity   0.9103
#> 2  Frobenius  24.6796
#> 3         KL   7.2063
#> 4  quadratic  54.1949
#> 5   spectral  13.1336
#> 6         TP  22.0000
#> 7         TN 370.0000
#> 8         FP  17.0000
#> 9         FN  26.0000
#> 10       TPR   0.4583
#> 11       FPR   0.0439
#> 12        F1   0.5057
#> 13       MCC   0.4545

Reference