# Sparse Bayesian Learning Algorithms Revisited: From Learning Majorizers to Structured Algorithmic Learning using Neural Networks

arXiv: https://arxiv.org/abs/2604.02513 · HTML: https://mlsanity.com/paper/2604.02513/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 57 references that are in the map.
- First posted on arXiv 2 Apr 2026.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Maximal Sparsity with Deep Networks?](https://mlsanity.com/paper/1605.01636/) (2016)
- [Improved Bounds on Neural Complexity for Representing Piecewise Linear Functions](https://mlsanity.com/paper/2210.07236/) (2022)
- [Robust Stochastically-Descending Unrolled Networks](https://mlsanity.com/paper/2312.15788/) (2023)
- [From Bayesian Sparsity to Gated Recurrent Nets](https://mlsanity.com/paper/1706.02815/) (2017)
- [ResNEsts and DenseNEsts: Block-based DNN Models with Improved Representation Guarantees](https://mlsanity.com/paper/2111.05496/) (2021)
- [Deep Learning-based Channel Estimation for Wideband Hybrid MmWave Massive MIMO](https://mlsanity.com/paper/2205.05202/) (2022)
- [Maximum Likelihood-based Gridless DoA Estimation Using Structured Covariance Matrix Recovery and SBL with Grid Refinement](https://mlsanity.com/paper/2210.03266/) (2022)
- [Type I and Type II Bayesian Methods for Sparse Signal Recovery using Scale Mixtures](https://mlsanity.com/paper/1507.05087/) (2015)
- [Learned-SBL: A Deep Learning Architecture for Sparse Signal Recovery](https://mlsanity.com/paper/1909.08185/) (2019)

## Abstract (arXiv)

Sparse Bayesian Learning is one of the most popular sparse signal recovery methods, and various algorithms exist under the SBL paradigm. However, given a performance metric and a sparse recovery problem, it is difficult to know a-priori the best algorithm to choose. This difficulty is in part due to a lack of a unified framework to derive SBL algorithms. We address this issue by first showing that the most popular SBL algorithms can be derived using the majorization-minimization (MM) principle, providing hitherto unknown convergence guarantees to this class of SBL methods. Moreover, we show that the two most popular SBL update rules not only fall under the MM framework but are both valid descent steps for a common majorizer, revealing a deeper analytical compatibility between these algorithms. Using this insight and properties from MM theory we expand the class of SBL algorithms, and address finding the best SBL algorithm via data within the MM framework. Second, we go beyond the MM framework by introducing the powerful modeling capabilities of deep learning to further expand the class of SBL algorithms, aiming to learn a superior SBL update rule from data. We propose a novel deep learning architecture that can outperform the classical MM based ones across different sparse recovery problems. Our architecture's complexity does not scale with the measurement matrix dimension, hence providing a unique opportunity to test generalization capability across different matrices. For parameterized dictionaries, this invariance allows us to train and test the model across different parameter ranges. We also showcase our model's ability to learn a functional mapping by its zero-shot performance on unseen measurement matrices. Finally, we test our model's performance across different numbers of snapshots, signal-to-noise ratios, and sparsity levels.