Related papers: Sparse Regression under Correlation and Weak Signa…
Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Meanwhile, a few recent works have provided theoretical justification and new…
Constructing confidence intervals for the coefficients of high-dimensional sparse linear models remains a challenge, mainly because of the complicated limiting distributions of the widely used estimators, such as the lasso. Several methods…
Precision matrices are crucial in many fields such as social networks, neuroscience, and economics, representing the edge structure of Gaussian graphical models (GGMs), where a zero in an off-diagonal position of the precision matrix…
We introduce a sparse high-dimensional regression approach that can incorporate prior information on the regression parameters and can borrow information across a set of similar datasets. Prior information may for instance come from…
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…
Classically, statistical datasets have a larger number of data points than features ($n > p$). The standard model of classical statistics caters for the case where data points are considered conditionally independent given the parameters.…
A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried…
This paper examines the effectiveness of a sparse Bayesian algorithm to estimate multivariate autoregressive coefficients when a large amount of background interference exists. This paper employs computer experiments to compare two methods…
Sample selection models are a widely used approach for correcting bias caused by data that are missing not at random. Their formulation requires specifying the variables that influence the outcome and those that drive the selection process.…
Quantile regression, a robust method for estimating conditional quantiles, has advanced significantly in fields such as econometrics, statistics, and machine learning. In high-dimensional settings, where the number of covariates exceeds…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
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…
We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we…
A greedy algorithm called Bayesian multiple matching pursuit (BMMP) is proposed to estimate a sparse signal vector and its support given $m$ linear measurements. Unlike the maximum a posteriori (MAP) support detection, which was proposed by…
During the past decade, shrinkage priors have received much attention in Bayesian analysis of high-dimensional data. This paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,…
We study the asymptotic properties of Deshpande et al.\ (2019)'s multivariate spike-and-slab LASSO (mSSL) procedure for simultaneous variable and covariance selection in the sparse multivariate linear regression problem. In that problem,…
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the…
Inference for high-dimensional logistic regression models using penalized methods has been a challenging research problem. As an illustration, a major difficulty is the significant bias of the Lasso estimator, which limits its direct…
The first Bayesian results for the sparse normal means problem were proven for spike-and-slab priors. However, these priors are less convenient from a computational point of view. In the meanwhile, a large number of continuous shrinkage…
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…