Adaptive posterior concentration rates for sparse high-dimensional linear regression with random design and unknown error variance
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Abstract (arXiv)
This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and analyze its concentration rates, demonstrating adaptiveness to the unknown sparsity level of the regression coefficient vector. Furthermore, we extend our investigation to establish concentration outcomes for parameter estimation using specific distance measures. These findings are in line with recent discoveries in frequentist studies. Additionally, by employing techniques to address model misspecification through a fractional posterior, we broaden our analysis through oracle inequalities to encompass the critical aspect of model misspecification for the regular posterior. Our novel findings are demonstrated using two different types of sparsity priors: a shrinkage prior and a spike-and-slab prior.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 23 of its 69 references that are in the map. First posted on arXiv 29 May 2024.
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