# General Pruning Criteria for Fast SBL

arXiv: https://arxiv.org/abs/2509.21572 · HTML: https://mlsanity.com/paper/2509.21572/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 20 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Builds on (most cited first, 5 of 5)

- [Revisiting Bayesian Blind Deconvolution](https://mlsanity.com/paper/1305.2362/) (2013)
- [Sparse Bayesian Learning via Stepwise Regression](https://mlsanity.com/paper/2106.06095/) (2021)
- [An Iterative Receiver for OFDM With Sparsity-Based Parametric Channel Estimation](https://mlsanity.com/paper/1507.02954/) (2015)
- [Variational Inference of Structured Line Spectra Exploiting Group-Sparsity](https://mlsanity.com/paper/2303.03017/) (2023)
- [A Block-Sparse Bayesian Learning Algorithm with Dictionary Parameter Estimation for Multi-Sensor Data Fusion](https://mlsanity.com/paper/2503.12913/) (2025)

## Abstract (arXiv)

Sparse Bayesian learning (SBL) associates to each weight in the underlying linear model a hyperparameter by assuming that each weight is Gaussian distributed with zero mean and precision (inverse variance) equal to its associated hyperparameter. The method estimates the hyperparameters by marginalizing out the weights and performing (marginalized) maximum likelihood (ML) estimation. SBL returns many hyperparameter estimates to diverge to infinity, effectively setting the estimates of the corresponding weights to zero (i.e., pruning the corresponding weights from the model) and thereby yielding a sparse estimate of the weight vector. In this letter, we analyze the marginal likelihood as function of a single hyperparameter while keeping the others fixed, when the Gaussian assumptions on the noise samples and the weight distribution that underlies the derivation of SBL are weakened. We derive sufficient conditions that lead, on the one hand, to finite hyperparameter estimates and, on the other, to infinite ones. Finally, we show that in the Gaussian case, the two conditions are complementary and coincide with the pruning condition of fast SBL (F-SBL), thereby providing additional insights into this algorithm.