Related papers: Nonparametric Empirical Bayes Estimation and Testi…
Nonresponse weighting adjustment using propensity score is a popular method for handling unit nonresponse. However, including all available auxiliary variables into the propensity model can lead to inefficient and inconsistent estimation,…
Posterior sampling with the spike-and-slab prior [MB88], a popular multimodal distribution used to model uncertainty in variable selection, is considered the theoretical gold standard method for Bayesian sparse linear regression [CPS09,…
Inferring the parameters of a stochastic model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e. when distinct sets of parameters…
Numerous practical medical problems often involve data that possess a combination of both sparse and non-sparse structures. Traditional penalized regularizations techniques, primarily designed for promoting sparsity, are inadequate to…
We propose a novel adaptive empirical Bayesian method for sparse deep learning, where the sparsity is ensured via a class of self-adaptive spike-and-slab priors. The proposed method works by alternatively sampling from an adaptive…
Sparseness of the regression coefficient vector is often a desirable property, since, among other benefits, sparseness improves interpretability. In practice, many true regression coefficients might be negligibly small, but non-zero, which…
Simultaneous analysis of gene expression data and genetic variants is highly of interest, especially when the number of gene expressions and genetic variants are both greater than the sample size. Association of both causal genes and…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
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…
Nonresponse frequently arises in practice, and simply ignoring it may lead to erroneous inference. Besides, the number of collected covariates may increase as the sample size in modern statistics, so parametric imputation or propensity…
This paper suggests a nonparametric scheme to find the sparse solution of the underdetermined system of linear equations in the presence of unknown impulsive or non-Gaussian noise. This approach is robust against any variations of the noise…
This paper presents the use of spike-and-slab (SS) priors for discovering governing differential equations of motion of nonlinear structural dynamic systems. The problem of discovering governing equations is cast as that of selecting…
Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…
Using a low-dimensional parametrization of signals is a generic and powerful way to enhance performance in signal processing and statistical inference. A very popular and widely explored type of dimensionality reduction is sparsity; another…
We consider exact algorithms for Bayesian inference with model selection priors (including spike-and-slab priors) in the sparse normal sequence model. Because the best existing exact algorithm becomes numerically unstable for sample sizes…
Spike-and-slab and horseshoe regression are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the…
The simultaneous estimation of many parameters based on data collected from corresponding studies is a key research problem that has received renewed attention in the high-dimensional setting. Many practical situations involve heterogeneous…
This paper presents a novel Bayesian approach for hyperspectral image unmixing. The observed pixels are modeled by a linear combination of material signatures weighted by their corresponding abundances. A spike-and-slab abundance prior is…
We revisit the problem of simultaneously testing the means of $n$ independent normal observations under sparsity. We take a Bayesian approach to this problem by introducing a scale-mixture prior known as the normal-beta prime (NBP) prior.…
A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…