Bayesian Inference using the Proximal Mapping: Uncertainty Quantification under Varying Dimensionality

2021/08/10 by Maoran Xu, Xu, Maoran, Hua Zhou +5 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Methodology (stat.ME) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2108.04851

openalex publication_date 2021/08/10 · openalex created_date 2021/08/16 · openalex updated_date 2026/07/28

Abstract

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of obtaining a point estimate via the optimization, it is much more challenging to quantify their uncertainty -- in the Bayesian framework, a major difficulty is that if assigning the prior associated with a p-dimensional measure, then there is zero posterior probability on any lower-dimensional subset with dimension d

Citations

• Semidefinite Programming

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