# Hierarchical Ensemble Kalman Methods with Sparsity-Promoting Generalized Gamma Hyperpriors

arXiv: https://arxiv.org/abs/2205.09322 · HTML: https://mlsanity.com/paper/2205.09322/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2022.

## Built on by (most cited first, 5 of 5)

- [Sampling via Gradient Flows in the Space of Probability Measures](https://mlsanity.com/paper/2310.03597/) (2023)
- [Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance](https://mlsanity.com/paper/2302.11024/) (2023)
- [Non-Asymptotic Analysis of Ensemble Kalman Updates: Effective Dimension and Localization](https://mlsanity.com/paper/2208.03246/) (2022)
- [Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2501.08501/) (2025)
- [Leveraging joint sparsity in hierarchical Bayesian learning](https://mlsanity.com/paper/2303.16954/) (2023)

## Abstract (arXiv)

This paper introduces a computational framework to incorporate flexible regularization techniques in ensemble Kalman methods for nonlinear inverse problems. The proposed methodology approximates the maximum a posteriori (MAP) estimate of a hierarchical Bayesian model characterized by a conditionally Gaussian prior and generalized gamma hyperpriors. Suitable choices of hyperparameters yield sparsity-promoting regularization. We propose an iterative algorithm for MAP estimation, which alternates between updating the unknown with an ensemble Kalman method and updating the hyperparameters in the regularization to promote sparsity. The effectiveness of our methodology is demonstrated in several computed examples, including compressed sensing and subsurface flow inverse problems.