相关论文: Bayesian Compressive Sensing Using Normal Product …

We characterize the measurement complexity of compressed sensing of signals drawn from a known prior distribution, even when the support of the prior is the entire space (rather than, say, sparse vectors). We show for Gaussian measurements…

Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…

Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…

The power prior is a popular tool for constructing informative prior distributions based on historical data. The method consists of raising the likelihood to a discounting factor in order to control the amount of information borrowed from…

Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…

This paper presents a sparse Bayesian learning (SBL) algorithm for linear inverse problems with a high order total variation (HOTV) sparsity prior. For the problem of sparse signal recovery, SBL often produces more accurate estimates than…

Gaussian Process Regression (GPR) is a powerful tool for nonparametric regression, but its application in a fully Bayesian fashion in high-dimensional settings is hindered by two primary challenges: the difficulty of variable selection and…

We propose a Bayesian approach to learn discriminative dictionaries for sparse representation of data. The proposed approach infers probability distributions over the atoms of a discriminative dictionary using a Beta Process. It also…

We consider the sparse high-dimensional linear regression model $Y=Xb+\epsilon$ where $b$ is a sparse vector. For the Bayesian approach to this problem, many authors have considered the behavior of the posterior distribution when, in truth,…

This paper considers a Bayesian approach for inclusion detection in nonlinear inverse problems using two known and popular push-forward prior distributions: the star-shaped and level set prior distributions. We analyze the convergence of…

We explore the use of generalized t priors on regression coefficients to help understand the nature of association signal within "hit regions" of genome-wide association studies. The particular generalized t distribution we adopt is a…

This work is concerned with uncertainty quantification in reduced-order dynamical system identification. Reduced-order models for system dynamics are ubiquitous in design and control applications and recent efforts focus on their…

We propose a scalable Bayesian preference learning method for jointly predicting the preferences of individuals as well as the consensus of a crowd from pairwise labels. Peoples' opinions often differ greatly, making it difficult to predict…

In this paper, we propose a sparse recovery algorithm called detection-directed (DD) sparse estimation using Bayesian hypothesis test (BHT) and belief propagation (BP). In this framework, we consider the use of sparse-binary sensing…

We propose a Machine Learning approach for optimal macroeconomic density forecasting in a high-dimensional setting where the underlying model exhibits a known group structure. Our approach is general enough to encompass specific forecasting…

The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…

In this paper, we investigate a Bayesian sparse reconstruction algorithm called compressive sensing via Bayesian support detection (CS-BSD). This algorithm is quite robust against measurement noise and achieves the performance of a minimum…

We propose a generalized double Pareto prior for Bayesian shrinkage estimation and inferences in linear models. The prior can be obtained via a scale mixture of Laplace or normal distributions, forming a bridge between the Laplace and…

We have utilized the non-conjugate Variational Bayesian (VB) method for the problem of the sparse Poisson regression model. To provide approximate conjugacy in the model, the likelihood is approximated by a quadratic function, yielding…

The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is…