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Title: A data-driven Bayesian graphical ridge estimator Authors:  Jarod Smith - University of Pretoria (South Africa) [presenting]
Mohammad Arashi - Ferdowsi University of Mashhad (Iran)
Andriette Bekker - University of Pretoria (South Africa)
Abstract: Bayesian methodologies prioritising accurate associations above sparsity in Gaussian graphical model (GGM) estimation remain relatively scarce in scientific literature. It is well accepted that the l2 penalty enjoys a smaller computational footprint in GGM estimation, whilst the $l_1$ penalty encourages sparsity in the estimand. The Bayesian adaptive graphical lasso prior is used as a departure point in the formulation of a computationally efficient graphical ridge-type prior for events where accurate associations are prioritised over sparse representations. A novel block Gibbs sampler for simulating precision matrices is constructed using a ridge-type penalisation. The Bayesian graphical ridge-type prior is extended to a Bayesian adaptive graphical ridge-type prior. Synthetic experiments indicate that the graphical ridge-type estimators enjoy computational efficiency, in moderate dimensions, and numerical performance, for relatively non-sparse precision matrices, when compared to their lasso counterparts. The adaptive graphical ridge-type estimator is applied to cell signalling data to infer key associations between phosphorylated proteins in human T-cell signalling. All computational workloads are carried out using the baygel R package.