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A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…

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,…

This article proposes a Bayesian approach to regression with a scalar response against vector and tensor covariates. Tensor covariates are commonly vectorized prior to analysis, failing to exploit the structure of the tensor, and resulting…

Due to its self-regularizing nature and its ability to quantify uncertainty, the Bayesian approach has achieved excellent recovery performance across a wide range of sparse signal recovery applications. However, most existing methods are…

This paper addresses computational challenges in estimating Quantile Regression with Selection (QRS). The estimation of the parameters that model self-selection requires the estimation of the entire quantile process several times. Moreover,…

This paper proposes a flexible Bayesian approach to multiple imputation using conditional Gaussian mixtures. We introduce novel shrinkage priors for covariate-dependent mixing proportions in the mixture models to automatically select the…

Applications of high-dimensional regression often involve multiple sources or types of covariates. We propose methodology for this setting, emphasizing the "wide data" regime with large total dimensionality p and sample size n<<p. We focus…

Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This…

The new class of Markov processes is proposed to realize the flexible shrinkage effects for the dynamic models. The transition density of the new process consists of two penalty functions, similarly to Bayesian fused LASSO in its functional…

Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We…

We introduce a new empirical Bayes approach for large-scale multiple linear regression. Our approach combines two key ideas: (i) the use of flexible "adaptive shrinkage" priors, which approximate the nonparametric family of scale mixture of…

We study a seemingly unexpected and relatively less understood overfitting aspect of a fundamental tool in sparse linear modeling - best subset selection, which minimizes the residual sum of squares subject to a constraint on the number of…

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…

High-dimensional spatially correlated covariates are common in regression models encountered in environmental sciences and other fields. In such models, the regression coefficients often exhibit a sparse structure with spatial dependence.…

Recurrent neural networks show state-of-the-art results in many text analysis tasks but often require a lot of memory to store their weights. Recently proposed Sparse Variational Dropout eliminates the majority of the weights in a…

In this paper, a sparse signal recovery algorithm using Bayesian linear regression with Cauchy prior (BLRC) is proposed. Utilizing an approximate expectation maximization(AEM) scheme, a systematic hyper-parameter updating strategy is…

We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian…

We introduce a new method of Bayesian wavelet shrinkage for reconstructing a signal when we observe a noisy version. Rather than making the common assumption that the wavelet coefficients of the signal are independent, we allow for the…

Survival analysis is an important area of medical research, yet existing models often struggle to balance simplicity with flexibility. Simple models require minimal adjustments but come with strong assumptions, while more flexible models…

In this paper, we review state-of-the-art methods for feature selection in statistics with an application-oriented eye. Indeed, sparsity is a valuable property and the profusion of research on the topic might have provided little guidance…