regularization
Definition
Regularization refers to a class of methods used in Gaussian graphical models to shrink estimated partial correlations toward zero, producing sparser network representations by treating small or spurious edges as absent. In the context of Bayesian estimation, regularization is achieved by setting the base covariance matrix to a diagonal or identity matrix, with the degrees of freedom parameter controlling the degree of shrinkage applied to covariance and correlation values. Because no single regularization method performs reliably across all conditions, the development of new approaches remains an active area, motivating generalized Bayesian frameworks capable of estimating regularized partial correlations across diverse data types, including binary, ordinal, and continuous variables.
Sources: Franco et al. (2024)
Related Terms
- Bayesian analysis (1 shared article)
- probabilistic graphical modeling (1 shared article)
- psychometrics (1 shared article)
Applications
Regularization and Bayesian Gaussian Graphical Models
Bayesian Gaussian graphical models incorporate regularization directly through prior specification, particularly by assigning an inverse Wishart prior to the covariance matrix with a diagonal base matrix, where the degrees of freedom determine the strength of shrinkage toward zero. The generalized approach introduced for these models extends this logic by parameterizing the lower-diagonal elements of the Cholesky decomposition matrix, allowing any zero-centered symmetric distribution to serve as a prior and thereby accommodating different degrees and forms of regularization across varied data types.
Sources: Franco et al. (2024)
Regularization and Partial Correlations
Regularization methods in Gaussian graphical models target the partial correlations derived from the concentration matrix, forcing coefficients that are small or likely spurious to exactly zero. Bayesian approaches achieve shrinkage by setting prior hyperparameters such that correlation estimates are pulled toward zero, with post-hoc procedures then used to determine which edges should be retained in the final network.
Sources: Franco et al. (2024)
