# Leveraging joint sparsity in hierarchical Bayesian learning

arXiv: https://arxiv.org/abs/2303.16954 · HTML: https://mlsanity.com/paper/2303.16954/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 56 references that are in the map.
- First posted on arXiv 29 Mar 2023.

## Builds on (most cited first, 11 of 11)

- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)
- [Coupling techniques for nonlinear ensemble filtering](https://mlsanity.com/paper/1907.00389/) (2019)
- [Generalized sparse Bayesian learning and application to image reconstruction](https://mlsanity.com/paper/2201.07061/) (2022)
- [Hierarchical Ensemble Kalman Methods with Sparsity-Promoting Generalized Gamma Hyperpriors](https://mlsanity.com/paper/2205.09322/) (2022)
- [A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors](https://mlsanity.com/paper/2111.13329/) (2021)
- [Bayesian neural network priors for edge-preserving inversion](https://mlsanity.com/paper/2112.10663/) (2021)
- [Sequential image recovery using joint hierarchical Bayesian learning](https://mlsanity.com/paper/2206.12745/) (2022)
- [Detecting edges from non-uniform Fourier data via sparse Bayesian learning](https://mlsanity.com/paper/1811.12220/) (2018)
- [Path-following methods for Maximum a Posteriori estimators in Bayesian hierarchical models: How estimates depend on hyperparameters](https://mlsanity.com/paper/2211.07113/) (2022)
- [Sequential edge detection using joint hierarchical Bayesian learning](https://mlsanity.com/paper/2302.14247/) (2023)

## Built on by (most cited first, 1 of 1)

- [Variational Bayesian Inference for Tensor Robust Principal Component Analysis](https://mlsanity.com/paper/2412.18717/) (2024)

## Abstract (arXiv)

We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed hyper-parameters to enforce joint sparsity. The resulting joint-sparsity-promoting priors are combined with existing Bayesian inference methods to generate a new family of algorithms. Our numerical experiments, which include a multi-coil magnetic resonance imaging application, demonstrate that our new approach consistently outperforms commonly used hierarchical Bayesian methods.