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We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…

A greedy algorithm is proposed for sparse-sensor selection in reduced-order sensing that contains correlated noise in measurement. The sensor selection is carried out by maximizing the determinant of the Fisher information matrix in a…

This paper presents a novel variational inference framework for deriving a family of Bayesian sparse Gaussian process regression (SGPR) models whose approximations are variationally optimal with respect to the full-rank GPR model enriched…

This paper extends the idea of decoupling shrinkage and sparsity for continuous priors to Bayesian Quantile Regression (BQR). The procedure follows two steps: In the first step, we shrink the quantile regression posterior through state of…

In the literature surrounding Bayesian penalized regression, the two primary choices of prior distribution on the regression coefficients are zero-mean Gaussian and Laplace. While both have been compared numerically and theoretically, there…

Penalized regression methods, such as $L_1$ regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is…

The information bottleneck framework provides a systematic approach to learning representations that compress nuisance information in the input and extract semantically meaningful information about predictions. However, the choice of a…

We propose a new method, {\it binary fused compressive sensing} (BFCS), to recover sparse piece-wise smooth signals from 1-bit compressive measurements. The proposed algorithm is a modification of the previous {\it binary iterative hard…

The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…

This paper shows how sparse, high-dimensional probability distributions could be represented by neurons with exponential compression. The representation is a novel application of compressive sensing to sparse probability distributions…

The deep image prior was recently introduced as a prior for natural images. It represents images as the output of a convolutional network with random inputs. For "inference", gradient descent is performed to adjust network parameters to…

Sparsity priors are commonly used in denoising and image reconstruction. For analysis-type priors, a dictionary defines a representation of signals that is likely to be sparse. In most situations, this dictionary is not known, and is to be…

This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…

The random dot product graph is a popular model for network data with extensions that accommodate dynamic (time-varying) networks. However, two significant deficiencies exist in the dynamic random dot product graph literature: (1) no…

Bayesian inference is known to provide a general framework for incorporating prior knowledge or specific properties into machine learning models via carefully choosing a prior distribution. In this work, we propose a new type of prior…

We present a sparse estimation and dictionary learning framework for compressed fiber sensing based on a probabilistic hierarchical sparse model. To handle severe dictionary coherence, selective shrinkage is achieved using a Weibull prior,…

In underwater acoustics, shallow water environments act as modal dispersive waveguides when considering low-frequency sources. In this context, propagating signals can be described as a sum of few modal components, each of them propagating…

This paper concerns the problem of 1-bit compressed sensing, where the goal is to estimate a sparse signal from a few of its binary measurements. We study a non-convex sparsity-constrained program and present a novel and concise analysis…

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…

Compressed sensing provides an efficient framework for reconstructing wave signals from reduced measurements. For multi-channel buoy data, the three displacement components exhibit intrinsic correlations, as wave motion contributes…