regularization
Definition
Regularization refers to a statistical technique that constrains or shrinks parameter estimates toward zero to address spurious correlations and improve model stability in graphical models. In Gaussian Graphical Models (GGMs), regularization methods such as graphical LASSO force small partial correlation coefficients to zero, controlled by a tuning parameter that determines the degree of sparsity in the resulting network graph. Bayesian approaches to regularization achieve this by setting hyperparameters of prior distributions to control the amount of shrinkage applied to covariance or correlation values, with higher values indicating stronger regularization.
Sources: Franco et al. (2024)
Related Terms
Applications
Regularization and Partial Correlations
Regularization techniques are specifically applied to partial correlations in Gaussian Graphical Models to identify and eliminate spurious relationships between variables. By forcing small partial correlation coefficients to zero through methods like graphical LASSO or Bayesian shrinkage priors, regularization helps distinguish genuine conditional dependencies from noise in the estimated network structure.
Sources: Franco et al. (2024)
Regularization and Network Sparsity
The degree of regularization in GGMs directly controls the sparsity of the resulting network graph, with lower regularization parameter values producing denser graphs containing more edges and higher values yielding sparser graphs with fewer connections.
Sources: Franco et al. (2024)
