Related papers: Log-Scale Shrinkage Priors and Adaptive Bayesian G…
We consider Markov chain Monte Carlo (MCMC) algorithms for Bayesian high-dimensional regression with continuous shrinkage priors. A common challenge with these algorithms is the choice of the number of iterations to perform. This is…
This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence…
We study high-dimensional Bayesian linear regression with a general beta prime distribution for the scale parameter. Under the assumption of sparsity, we show that appropriate selection of the hyperparameters in the beta prime prior leads…
The James-Stein estimator is an estimator of the multivariate normal mean and dominates the maximum likelihood estimator (MLE) under squared error loss. The original work inspired great interest in developing shrinkage estimators for a…
This paper argues that the half-Cauchy distribution should replace the inverse-Gamma distribution as a default prior for a top-level scale parameter in Bayesian hierarchical models, at least for cases where a proper prior is necessary. Our…
We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy tailed series priors. We illustrate it in a variety of settings, showing in particular that the corresponding Bayesian posterior…
Many real-life applications involve estimation of curves that exhibit complicated shapes including jumps or varying-frequency oscillations. Practical methods have been devised that can adapt to a locally varying complexity of an unknown…
We study the rate of convergence of posterior distributions in density estimation problems for log-densities in periodic Sobolev classes characterized by a smoothness parameter p. The posterior expected density provides a nonparametric…
We discuss a Bayesian hierarchical copula model for clusters of financial time series. A similar approach has been developed in recent paper. However, the prior distributions proposed there do not always provide a proper posterior. In order…
In high dimensional regression, global local shrinkage priors have gained significant traction for their ability to yield sparse estimates, improve parameter recovery, and support accurate predictive modeling. While recent work has explored…
In this work, we propose low-complexity adaptive biased estimation algorithms, called group-based shrinkage estimators (GSEs), for parameter estimation and interference suppression scenarios with mechanisms to automatically adjust the…
In recent years, various notions of capacity and complexity have been proposed for characterizing the generalization properties of stochastic gradient descent (SGD) in deep learning. Some of the popular notions that correlate well with the…
We consider estimation of a normal mean matrix under the Frobenius loss. Motivated by the Efron--Morris estimator, a generalization of Stein's prior has been recently developed, which is superharmonic and shrinks the singular values towards…
We develop a class of data-adaptive shrinkage estimators for high-dimensional covariance estimation in which the shrinkage target is a Reynolds projection of the sample covariance under a finite symmetry group selected from a candidate…
We investigate the problem of deriving adaptive posterior rates of contraction on $\mathbb{L}^{\infty}$ balls in density estimation. Although it is known that log-density priors can achieve optimal rates when the true density is…
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…
We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy…
We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of…
When developing risk prediction models, shrinkage methods are recommended, especially when the sample size is limited. Several earlier studies have shown that the shrinkage of model coefficients can reduce overfitting of the prediction…
Graphs have been commonly used to represent complex data structures. In models dealing with graph-structured data, multivariate parameters may not only exhibit sparse patterns but have structured sparsity and smoothness in the sense that…