Related papers: Fully Bayesian Penalized Regression with a General…
We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…
A hierarchical Bayesian approach that permits simultaneous inference for the regression coefficient matrix and the error precision (inverse covariance) matrix in the multivariate linear model is proposed. Assuming a natural ordering of the…
The Bayesian elastic net regression model is characterized by the regression coefficient prior distribution, the negative log density of which corresponds to the elastic net penalty function. While Markov chain Monte Carlo (MCMC) methods…
We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…
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…
Consider the {$\ell_{\alpha}$} regularized linear regression, also termed Bridge regression. For $\alpha\in (0,1)$, Bridge regression enjoys several statistical properties of interest such as sparsity and near-unbiasedness of the estimates…
We study the implementation of Automatic Differentiation Variational inference (ADVI) for Bayesian inference on regression models with bridge penalization. The bridge approach uses $\ell_{\alpha}$ norm, with $\alpha \in (0, +\infty)$ to…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
This article is concerned with the Bridge Regression, which is a special family in penalized regression with penalty function $\sum_{j=1}^{p}|\beta_j|^q$ with $q>0$, in a linear model with linear restrictions. The proposed restricted bridge…
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…
We develop a penalized likelihood estimation framework to estimate the structure of Gaussian Bayesian networks from observational data. In contrast to recent methods which accelerate the learning problem by restricting the search space, our…
This paper is devoted to the estimation of a partial graphical model with a structural Bayesian penalization. Precisely, we are interested in the linear regression setting where the estimation is made through the direct links between…
The identification of predictive biomarkers from a large scale of covariates for subgroup analysis has attracted fundamental attention in medical research. In this article, we propose a generalized penalized regression method with a novel…
We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…
This paper considers equity premium prediction, for which mean regression can be problematic due to heteroscedasticity and heavy-tails of the error. We show advantages of quantile predictions using a novel penalized quantile regression that…
We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient…
We develop a penalized two-pass regression with time-varying factor loadings. The penalization in the first pass enforces sparsity for the time-variation drivers while also maintaining compatibility with the no-arbitrage restrictions by…
The SLOPE estimates regression coefficients by minimizing a regularized residual sum of squares using a sorted-$\ell_1$-norm penalty. The SLOPE combines testing and estimation in regression problems. It exhibits suitable variable selection…
The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which…