mlsanityData to 7 Oct 2026

Bayesian linear regression with sparse priors

arXiv 1403.0735 ↗First posted 4 Mar 2014math.ST stat.ME stat.THcited by 40

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Abstract (arXiv)

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the posterior distribution is shown to contract at the optimal rate for recovery of the unknown sparse vector, and to give optimal prediction of the response vector. It is also shown to select the correct sparse model, or at least the coefficients that are significantly different from zero. The asymptotic shape of the posterior distribution is characterized and employed to the construction and study of credible sets for uncertainty quantification.

Key facts. Cited by 40 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Mar 2014.

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Citing papers per year: 2021: 7; 2022: 8; 2023: 6; 2024: 9; 2025: 5; 2026: 5.

40 papers.

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  1. 2021Identifiable Deep Generative Models via Sparse Decodingcited by 54
  2. 2022Thompson Sampling for High-Dimensional Sparse Linear Contextual Banditscited by 16
  3. 2024Bayesian Concept Bottleneck Models with LLM Priorscited by 16
  4. 2021Variational Inference in high-dimensional linear regressioncited by 10
  5. 2022The price of ignorance: how much does it cost to forget noise structure in low-rank matrix estimation?cited by 9
  6. 2023Masked Bayesian Neural Networks : Theoretical Guarantee and its Posterior Inferencecited by 9
  7. 2021Fast and Scalable Spike and Slab Variable Selection in High-Dimensional Gaussian Processescited by 7
  8. 2022Asymptotic Properties for Bayesian Neural Network in Besov Spacecited by 7
  9. 2024Misclassification bounds for PAC-Bayesian sparse deep learningcited by 7
  10. 2021Performance of Bayesian linear regression in a model with mismatchcited by 6
  11. 2024A sparse PAC-Bayesian approach for high-dimensional quantile predictioncited by 6
  12. 2022Scalable Spike-and-Slabcited by 5
28 more
  1. 2022Robust Methods for High-Dimensional Linear Learningcited by 5
  2. 2024Bayesian Joint Additive Factor Models for Multiview Learningcited by 5
  3. 2023FedBIAD: Communication-Efficient and Accuracy-Guaranteed Federated Learning with Bayesian Inference-Based Adaptive Dropoutcited by 4
  4. 2025High-dimensional Bayesian Tobit regression for censored response with Horseshoe priorcited by 4
  5. 2021Spike and slab Bayesian sparse principal component analysiscited by 3
  6. 2021A fast asynchronous MCMC sampler for sparse Bayesian inferencecited by 3
  7. 2023Hierarchical shrinkage Gaussian processes: applications to computer code emulation and dynamical system recoverycited by 3
  8. 2021Sparse online variational Bayesian regressioncited by 2
  9. 2022Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithmcited by 2
  10. 2022On the optimization and pruning for Bayesian deep learningcited by 2
  11. 2024Covariate-Elaborated Robust Partial Information Transfer with Conditional Spike-and-Slab Priorcited by 2
  12. 2025Handling bounded response in high dimensions: a Horseshoe prior Bayesian Beta regression approachcited by 2
  13. 2022Masked Bayesian Neural Networks : Computation and Optimalitycited by 1
  14. 2024Adaptive posterior concentration rates for sparse high-dimensional linear regression with random design and unknown error variancecited by 1
  15. 2024Isoperimetry is All We Need: Langevin Posterior Sampling for RL with Sublinear Regretcited by 1
  16. 2025Correcting Noisy Multilabel Predictions: Modeling Label Noise through Latent Space Shiftscited by 1
  17. 2026Stability of Sequential and Parallel Coordinate Ascent Variational Inferencecited by 1
  18. 2023Bayesian Analysis for Over-parameterized Linear Model via Effective Spectracited by 0
  19. 2023From Estimation to Sampling for Bayesian Linear Regression with Spike-and-Slab Priorcited by 0
  20. 2023A statistical perspective on algorithm unrolling models for inverse problemscited by 0
  21. 2024High-dimensional prediction for count response via sparse exponential weightscited by 0
  22. 2024Bayesian penalized empirical likelihood and Markov Chain Monte Carlo samplingcited by 0
  23. 2025SpinSVAR: Estimating Structural Vector Autoregression Assuming Sparse Inputcited by 0
  24. 2025Time-varying Factor Augmented Vector Autoregression with Grouped Sparse Autoencodercited by 0
  25. 2026Spectral Bayesian Regression on the Spherecited by 0
  26. 2026Joint Model and Data Sparsification via the Marginal Likelihoodcited by 0
  27. 2026Beyond Global Divergences: A Local-Mass Perspective on Bayesian Inferencecited by 0
  28. 2026Sparsity by Default: The Theory and Practice of ARD in Gaussian Process Regression for Variable Selectioncited by 0