Investigate sparsity-promoting properties of group and heavy-tailed hyperpriors

Investigate the sparsity-promoting properties of broader classes of group or heavy-tailed hyperpriors, including Student’s t priors, within the empirical Bayes framework for conditional Gaussian models, and determine how these priors influence the sparsity of the estimated hyperparameters.

Background

The paper analyzes how hyperpriors from the generalized Gamma family affect sparsity and stability in empirical Bayes inference, showing that half-Laplace and half-generalized Gaussian (with shape parameter 0<p<1) strongly promote sparsity while improving robustness to noise.

Beyond these families, heavy-tailed and group-structured hyperpriors are widely used in Bayesian modeling and may offer different sparsity and stability trade-offs. A systematic investigation in the empirical Bayes setting remains to be carried out, particularly for priors like Student’s t that are known to induce strong shrinkage with heavy tails.

References

Several directions remain open for future work. Second, we plan to investigate the sparsity-promoting properties of broader classes of group or heavy-tailed hyperpriors, such as the Student’s t prior.

— Sparsity via Hyperpriors: A Theoretical and Algorithmic Study under Empirical Bayes Framework (2511.06235 - Li et al., 9 Nov 2025) in Section 6 (Conclusions)