2014/01/11 by Xin Yuan, Vinayak Rao, Yuan, Xin +5
Computer Science · Engineering · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Bayesian inference #Bayesian probability #Combinatorics #Computer science #Dual polyhedron #Expectation–maximization algorithm #FOS: Computer and information sciences #Gaussian #Gaussian process #Image and Signal Denoising Methods #Inference #Machine Learning (stat.ML) #Markov chain Monte Carlo #Mathematics #Maximum likelihood #Numerical methods in inverse problems #Physics #Point process #Prior probability #Shrinkage #Sparse and Compressive Sensing Techniques #Sparse approximation #Statistics #Wavelet #stat.ML
paper · pdf · doi:10.48550/arxiv.1401.2497
published in arXiv (Cornell University) (Cornell University) · 11 pages, 5 figures
arxiv created 2014/01/11 · openalex publication_date 2014/01/11 · arxiv updated 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A new shrinkage-based construction is developed for a compressible vector \boldsymbolx∈ℝn, for cases in which the components of \xv are naturally associated with a tree structure. Important examples are when \xv corresponds to the coefficients of a wavelet or block-DCT representation of data. The method we consider in detail, and for which numerical results are presented, is based on increments of a gamma process. However, we demonstrate that the general framework is appropriate for many other types of shrinkage priors, all within the Lévy process family, with the gamma process a special case. Bayesian inference is carried out by approximating the posterior with samples from an MCMC algorithm, as well as by constructing a heuristic variational approximation to the posterior. We also consider expectation-maximization (EM) for a MAP (point) solution. State-of-the-art results are manifested for compressive sensing and denoising applications, the latter with spiky (non-Gaussian) noise.