Package 'AdaptiveGlasso'

Fit an adaptive graphical lasso model

Description

Fits an adaptive graphical lasso model for sparse precision-matrix and network estimation. The procedure combines ridge stabilization, an initial graphical lasso estimate, adaptive edge-specific penalties, and a final weighted graphical lasso estimate.

Usage

adaptive_glasso(
  x,
  ridge = 0.1,
  d = 0.32,
  lambda = NULL,
  lam.min.ratio = 0.01,
  nfolds = 5L,
  standardize = TRUE,
  seed = 123L,
  penalize_diagonal = TRUE,
  tol = 1e-04,
  maxit = 10000L
)

Arguments

x	Numeric matrix or data frame with observations in rows and variables in columns.
ridge	Non-negative ridge stabilization constant added to the diagonal of the sample covariance matrix. Default is 0.10.
d	Positive stabilization constant used in the adaptive weights $w_{ij} = 1/(|\hat{\omega}^{init}_{ij}| + d)$. Default is 0.32.
lambda	Optional positive regularization parameter. If NULL, lambda is selected automatically by cross-validation using CVglasso. If a positive numeric value is supplied, that fixed value is used and cross-validation is skipped.
lam.min.ratio	Minimum-to-maximum lambda ratio used by CVglasso when lambda = NULL. Default is 0.01.
nfolds	Number of cross-validation folds used when lambda = NULL. Default is 5.
standardize	Logical; if TRUE, variables are standardized before fitting. Default is TRUE.
seed	Optional integer seed used for reproducibility of cross-validation when lambda = NULL. Default is 123.
penalize_diagonal	Logical; whether diagonal precision-matrix elements are penalized. Default is TRUE, matching the fitting procedure used in the motivating analysis.
tol	Positive convergence tolerance passed to the graphical lasso fitting routines. Default is 1e-4.
maxit	Maximum number of graphical lasso iterations. Default is 10000.

Details

The sample covariance matrix is first ridge-stabilized as

$S_{\delta} = S + \delta I,$

where ridge corresponds to $\delta$.

An initial graphical lasso estimate is then used to construct the adaptive weights

$w_{ij} = \frac{1}{|\hat{\omega}^{init}_{ij}| + d},$

followed by the edge-specific penalties

$\rho_{ij} = \lambda w_{ij}.$

The value of lambda can be handled in two ways:

• lambda = NULL: lambda is selected automatically by cross-validation using CVglasso.

• ⁠lambda =⁠ a positive numeric value: the supplied value is used directly and cross-validation is not performed.

The method can be applied when the number of observations is smaller than, equal to, or larger than the number of variables.

Value

An object of class "adaptive_glasso_fit" containing the fitted precision and covariance matrices, adjacency matrix, initial precision estimate, adaptive weights, adaptive penalty matrix, selected or supplied lambda, ridge and adaptive stabilization constants, cross-validation results when applicable, and fitting diagnostics.

Examples

set.seed(123)

x <- matrix(
  rnorm(60 * 6),
  nrow = 60,
  ncol = 6
)

# Use a fixed lambda: cross-validation is not performed
fit <- adaptive_glasso(
  x,
  lambda = 0.195237
)

fit
coef(fit, type = "precision")

# Select lambda automatically by cross-validation
fit_cv <- adaptive_glasso(
  x,
  lambda = NULL,
  nfolds = 3
)

fit_cv$lambda

---

Extract matrices from an adaptive graphical lasso fit

Description

Extract matrices from an adaptive graphical lasso fit

Usage

## S3 method for class 'adaptive_glasso_fit'
coef(
  object,
  type = c("precision", "adjacency", "weights", "penalty", "covariance"),
  ...
)

Arguments

object	An object returned by adaptive_glasso().
type	Matrix to return.
...	Additional arguments; currently unused.

Value

A matrix.

---

Print an adaptive graphical lasso fit

Description

Print an adaptive graphical lasso fit

Usage

## S3 method for class 'adaptive_glasso_fit'
print(x, ...)

Arguments

x	An object returned by adaptive_glasso().
...	Additional arguments; currently unused.

Value

The fitted object, invisibly.

---