Related papers: The Predictive Lasso
We propose a greedy mixture reduction algorithm which is capable of pruning mixture components as well as merging them based on the Kullback-Leibler divergence (KLD). The algorithm is distinct from the well-known Runnalls' KLD based method…
Spatial econometric research typically relies on the assumption that the spatial dependence structure is known in advance and is represented by a deterministic spatial weights matrix. Contrary to classical approaches, we investigate the…
In multi-state models based on high-dimensional data, effective modeling strategies are required to determine an optimal, ideally parsimonious model. In particular, linking covariate effects across transitions is needed to conduct joint…
In a first part, we present a mathematical analysis of a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a stochastic boundary value problem from a prior probability…
We develop a fully automatic Bayesian Lasso via variational inference. This is a scalable procedure for approximating the posterior distribution. Special attention is driven to the knot selection in regression spline. In order to carry…
Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…
We introduce a novel approach for estimating Latent Dirichlet Allocation (LDA) parameters from collapsed Gibbs samples (CGS), by leveraging the full conditional distributions over the latent variable assignments to efficiently average over…
The least absolute shrinkage and selection operator (LASSO) for linear regression exploits the geometric interplay of the $\ell_2$-data error objective and the $\ell_1$-norm constraint to arbitrarily select sparse models. Guiding this…
We introduce a new computational framework for estimating parameters in generalized generalized linear models (GGLM), a class of models that extends the popular generalized linear models (GLM) to account for dependencies among observations…
Currently several Bayesian approaches are available to estimate large sparse precision matrices, including Bayesian graphical Lasso (Wang, 2012), Bayesian structure learning (Banerjee and Ghosal, 2015), and graphical horseshoe (Li et al.,…
Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…
Motivated by the increasing use of and rapid changes in array technologies, we consider the prediction problem of fitting a linear regression relating a continuous outcome $Y$ to a large number of covariates $\mathbf {X}$, for example,…
In many problems involving generalized linear models, the covariates are subject to measurement error. When the number of covariates p exceeds the sample size n, regularized methods like the lasso or Dantzig selector are required. Several…
Unlike the ordinary least-squares (OLS) estimator for the linear model, a ridge regression linear model provides coefficient estimates via shrinkage, usually with improved mean-square and prediction error. This is true especially when the…
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…
In the sparse linear regression setting, we consider testing the significance of the predictor variable that enters the current lasso model, in the sequence of models visited along the lasso solution path. We propose a simple test statistic…
The projection predictive variable selection is a decision-theoretically justified Bayesian variable selection approach achieving an outstanding trade-off between predictive performance and sparsity. Its projection problem is not easy to…
Despite the abundance of methods for variable selection and accommodating spatial structure in regression models, there is little precedent for incorporating spatial dependence in covariate inclusion probabilities for regionally varying…
In exciting new work, Bertsimas et al. (2016) showed that the classical best subset selection problem in regression modeling can be formulated as a mixed integer optimization (MIO) problem. Using recent advances in MIO algorithms, they…
We investigate predictive densities for multivariate normal models with unknown mean vectors and known covariance matrices. Bayesian predictive densities based on shrinkage priors often have complex representations, although they are…