ggm_search {GGMnonreg}

Gaussian graphical model: automated search

Description

Data mining to learn the graph.

Usage

ggm_search(
  x,
  IC = "BIC",
  type = "neighborhood_selection",
  method = "forward",
  n = NULL
)

Arguments

x

A data matrix of dimensions n (observations) by p (nodes) or a correlation matrix of dimensions p by p.

IC

Character string. The desired information criterion. Options include "AIC" and "BIC" (default).

type

Character string. Which search method should be used? The options included "regression" and "approx_L0". See details.

method

Character string. The desired subset selection method Options includes "forward" (default), "backward", and "exhaustive".

n

Integer. Sample size. Required if a correlation matrix is provided.

Details

type = "neighborhood_selection" was described in Williams et al. (2019) and type = "approx_L0" was described in Williams (2020). The penalty for type = "approx_L0" is called seamless L0 (Dicker et al. 2013)

Value

An object of class ggm_search, including wadj (weighted adjacency matrix) and adj (adjacency matrix).

Note

type = "neighborhood_selection" employs multiple regression to estimate the graph (requires the data), whereas type = "approx_L0" directly estimates the precision matrix (data or a correlation matrix are acceptable). If data is provided and type = "approx_L0", by default Pearson correlations are used. For another correlation coefficient, provide the desired correlation matrix.

type = "approx_L0" is a continuous approximation to (non-regularized) best subset model selection. This is accomplished by using regularization, but the penalty (approximately) mimics non-regularized estimation.

References

Dicker L, Huang B, Lin X (2013). “Variable selection and estimation with the seamless-L 0 penalty.” Statistica Sinica, 929–962.

Williams DR (2020). “Beyond Lasso: A Survey of Nonconvex Regularization in Gaussian Graphical Models.” PsyArXiv. doi: 10.31234/osf.io/ad57p, https://doi.org/10.31234/osf.io/ad57p.

Williams DR, Rhemtulla M, Wysocki AC, Rast P (2019). “On nonregularized estimation of psychological networks.” Multivariate behavioral research, 54(5), 719–750. doi: 10.1080/00273171.2019.1575716, https://doi.org/10.1080/00273171.2019.1575716.

Examples

# data
Y <- ptsd

# search data
fit <- ggm_search(Y)