Related papers: Learning from a lot: Empirical Bayes in high-dimen…

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and…

Empirical Bayes inference is based on estimation of the parameters of an a priori distribution from the observed data. The estimation technique of the parameters of the prior, called hyperparameters, is based on the marginal distribution…

We consider inventory decisions with many items, each of which has Poisson demand. The rate of demand for individual items is estimated on the basis of observations of past demand. The problem is to determine the items to hold in stock and…

In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity,…

We demonstrate how data fission, a method for creating synthetic replicates from single observations, can be applied to empirical Bayes estimation. This extends recent work on empirical Bayes with multiple replicates to the classical…

Joint Bayesian factor models are popular for characterizing relationships between multivariate correlated predictors and a response variable. Standard models assume that all variables, including both the predictors and the response, are…

In applications of Bayesian procedures, once a class of priors has been chosen, it may be tempting to fix the prior's hyperparameters from the data, in an empirical Bayes (EB) fashion, usually by their maximum marginal likelihood estimates…

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…

Bayesian predictive inference analyzes a dataset to make predictions about new observations. When a model does not match the data, predictive accuracy suffers. We develop population empirical Bayes (POP-EB), a hierarchical framework that…

Few-shot learning aims to train efficient predictive models with a few examples. The lack of training data leads to poor models that perform high-variance or low-confidence predictions. In this paper, we propose to meta-learn the ensemble…

We consider the problem of statistical inference on parameters of a target population when auxiliary observations are available from related populations. We propose a flexible empirical Bayes approach that can be applied on top of any…

Multi-level normal hierarchical models, also interpreted as mixed effects models, play an important role in developing statistical theory in multi-parameter estimation for a wide range of applications. In this article, we propose a novel…

A common task in high-throughput biology is to screen for associations across thousands of units of interest, e.g., genes or proteins. Often, the data for each unit are modeled as Gaussian measurements with unknown mean and variance and are…

Bayesian Optimization is methodology used in statistical modelling that utilizes a Gaussian process prior distribution to iteratively update a posterior distribution towards the true distribution of the data. Finding unbiased informative…

We propose a new empirical Bayes approach for inference in the $p \gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a…

A novel data-driven methodology is presented for the joint selection of prior parameters for both fixed and random effects in Linear Mixed Models (LMMs). This approach facilitates the estimation of complex random-effects structures, as well…

We revisit empirical Bayes in the absence of a tractable likelihood function, as is typical in scientific domains relying on computer simulations. We investigate how the empirical Bayesian can make use of neural density estimators first to…

We consider the problem of empirical Bayes estimation of multiple variances when provided with sample variances. Assuming an arbitrary prior on the variances, we derive different versions of the Bayes estimators using different loss…

The recent literature on deep learning offers new tools to learn a rich probability distribution over high dimensional data such as images or sounds. In this work we investigate the possibility of learning the prior distribution over neural…

We develop an empirical Bayes procedure for estimating the cell means in an unbalanced, two-way additive model with fixed effects. We employ a hierarchical model, which reflects exchangeability of the effects within treatment and within…