# On The Sparse Bayesian Learning Of Linear Models

arXiv: https://arxiv.org/abs/1502.03416 · HTML: https://mlsanity.com/paper/1502.03416/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2015.

## Built on by (most cited first, 2 of 2)

- [Probabilistic Unrolling: Scalable, Inverse-Free Maximum Likelihood Estimation for Latent Gaussian Models](https://mlsanity.com/paper/2306.03249/) (2023)
- [An Efficient Algorithm for Clustered Multi-Task Compressive Sensing](https://mlsanity.com/paper/2310.00420/) (2023)

## Abstract (arXiv)

This work is a re-examination of the sparse Bayesian learning (SBL) of linear regression models of Tipping (2001) in a high-dimensional setting. We propose a hard-thresholded version of the SBL estimator that achieves, for orthogonal design matrices, the non-asymptotic estimation error rate of σ√slog p/√n, where n is the sample size, p the number of regressors, σ is the regression model standard deviation, and s the number of non-zero regression coefficients. We also establish that with high-probability the estimator identifies the non-zero regression coefficients. In our simulations we found that sparse Bayesian learning regression performs better than lasso (Tibshirani (1996)) when the signal to be recovered is strong.