Related papers: Singular Value Shrinkage Priors for Bayesian Predi…
We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…
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…
Prediction of a vector of ordered parameters or part of it arises naturally in the context of Small Area Estimation (SAE). For example, one may want to estimate the parameters associated with the top ten areas, the best or worst area, or a…
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…
We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…
We examine the effect of a prior that favours low values of fine-tuning on Bayesian multi-dimensional fits of the constrained minimal supersymmetric standard model (CMSSM or mSUGRA) to current data. The dark matter relic density, the…
Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t distributed measurement noise are presented. The proposed algorithms improve upon our earlier proposed filter and smoother using the mean field…
A new shrinkage-based construction is developed for a compressible vector $\boldsymbol{x}\in\mathbb{R}^n$, for cases in which the components of $\xv$ are naturally associated with a tree structure. Important examples are when $\xv$…
The possibility of improving on the usual multivariate normal confidence was first discussed in Stein (1962). Using the ideas of shrinkage, through Bayesian and empirical Bayesian arguments, domination results, both analytic and numerical,…
This paper studies the related problems of prediction, covariance estimation, and principal component analysis for the spiked covariance model with heteroscedastic noise. We consider an estimator of the principal components based on…
Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…
We consider a high-dimensional sparse normal means model where the goal is to estimate the mean vector assuming the proportion of non-zero means is unknown. We model the mean vector by a one-group global-local shrinkage prior belonging to a…
In this article, we investigate certain asymptotic optimality properties of a very broad class of one-group continuous shrinkage priors for simultaneous estimation and testing of a sparse normal mean vector. Asymptotic optimality of Bayes…
If we have an unbiased estimate of some parameter of interest, then its absolute value is positively biased for the absolute value of the parameter. This bias is large when the signal-to-noise ratio (SNR) is small, and it becomes even…
Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…
This paper introduces a novel Bayesian approach for variable selection in high-dimensional and potentially sparse regression settings. Our method replaces the indicator variables in the traditional spike and slab prior with continuous,…
Neural networks are the cornerstone of modern machine learning, yet can be difficult to interpret, give overconfident predictions and are vulnerable to adversarial attacks. Bayesian neural networks (BNNs) provide some alleviation of these…
A common strategy for sparse linear regression is to introduce regularization, which eliminates irrelevant features by letting the corresponding weights be zeros. However, regularization often shrinks the estimator for relevant features,…
Many applications involve estimating the mean of multiple binomial outcomes as a common problem -- assessing intergenerational mobility of census tracts, estimating prevalence of infectious diseases across countries, and measuring…
As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…