Related papers: Empirical Bayes shrinkage (mostly) does not correc…

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…

This book chapter introduces regression approaches and regression adjustment for Approximate Bayesian Computation (ABC). Regression adjustment adjusts parameter values after rejection sampling in order to account for the imperfect match…

In a linear regression model with random design, we consider a family of candidate models from which we want to select a `good' model for prediction out-of-sample. We fit the models using block shrinkage estimators, and we focus on the…

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…

A 'Winner's Curse' arises in large-scale online experimentation platforms when the same experiments are used to both select treatments and evaluate their effects. In these settings, classical difference-in-means estimators of treatment…

Many modern computational approaches to classical problems in quantitative finance are formulated as empirical loss minimization (ERM), allowing direct applications of classical results from statistical machine learning. These methods,…

The exponential distribution is applied in a very wide variety of statistical procedures. Among the most prominent applications are those in the field of life testing and reliability theory. When there are two record samples available for…

We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…

In machine learning models, the estimation of errors is often complex due to distribution bias, particularly in spatial data such as those found in environmental studies. We introduce an approach based on the ideas of importance sampling to…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

We present a linear regression method for predictions on a small data set making use of a second possibly biased data set that may be much larger. Our method fits linear regressions to the two data sets while penalizing the difference…

Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…

We discuss the use of empirical Bayes for data integration, in the sense of transfer learning. Our main interest is in settings where one wishes to learn structure (e.g. feature selection) and one only has access to incomplete data from…

While the performance of machine learning systems has experienced significant improvement in recent years, relatively little attention has been paid to the fundamental question: to what extent can we improve our models? This paper provides…

The widespread availability of high-dimensional biological data has made the simultaneous screening of many biological characteristics a central problem in computational biology and allied sciences. While the dimensionality of such datasets…

The problem of estimating a high-dimensional sparse vector $\boldsymbol{\theta} \in \mathbb{R}^n$ from an observation in i.i.d. Gaussian noise is considered. The performance is measured using squared-error loss. An empirical Bayes shrinkage…

In this paper, we apply shrinkage strategies to estimate regression coefficients efficiently for the high-dimensional multiple regression model, where the number of samples is smaller than the number of predictors. We assume in the sparse…

In this paper, we consider the multicollinearity problem in the gamma regression model when model parameters are linearly restricted. The linear restrictions are available from prior information to ensure the validity of scientific theories…

For some variants of regression models, including partial, measurement error or error-in-variables, latent effects, semi-parametric and otherwise corrupted linear models, the classical parametric tests generally do not perform well. Various…

We consider statistical inference for errors-in-variables regression models with dependent observations under the high dimensionality of the error covariance matrix. It is tempting to prewhiten the model and data that had led to efficient…