Related papers: Bias correction in a multivariate normal regressio…
Random matrix theory has proven to be a valuable tool in analyzing the generalization of linear models. However, the generalization properties of even two-layer neural networks trained by gradient descent remain poorly understood. To…
In this paper we consider an extension of the beta regression model proposed by Ferrari and Cribari-Neto (2004). We extend their model in two different ways, first, we let the regression structure be nonlinear, second, we allow a regression…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty…
In this paper, we study a generalization of the two-groups model in the presence of covariates --- a problem that has recently received much attention in the statistical literature due to its applicability in multiple hypotheses testing…
In this paper, we propose a parameter space augmentation approach that is based on "intentionally" introducing a pseudo-nuisance parameter into generalized linear models for the purpose of variance reduction. We first consider the parameter…
We provide an analytical framework for balanced realization model order reduction of linear control systems which depend on an unknown parameter. Besides recovering known results for the first order corrections, we obtain explicit novel…
The explorations of models beyond the Standard Model (BSM) naturally involve scans over the unknown BSM parameters. On the other hand, high precision predictions require calculations at the loop-level and thus a renormalization of (some of)…
Purpose: To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cram\'er-Rao bound. Theory and Methods: We generalize the mean squared error loss to control the bias and…
This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
We consider multi-response and multitask regression models, where the parameter matrix to be estimated is expected to have an unknown grouping structure. The groupings can be along tasks, or features, or both, the last one indicating a…
This paper investigates the use of regularization priors in the context of treatment effect estimation using observational data where the number of control variables is large relative to the number of observations. First, the phenomenon of…
Post-Double-Lasso is becoming the most popular method for estimating linear regression models with many covariates when the purpose is to obtain an accurate estimate of a parameter of interest, such as an average treatment effect. However,…
We investigate methods for penalized regression in the presence of missing observations. This paper introduces a method for estimating the parameters which compensates for the missing observations. We first, derive an unbiased estimator of…
In this article, we develop a distributed variable screening method for generalized linear models. This method is designed to handle situations where both the sample size and the number of covariates are large. Specifically, the proposed…
Due to the curse of dimensionality, estimation in a multidimensional nonparametric regression model is in general not feasible. Hence, additional restrictions are introduced, and the additive model takes a prominent place. The restrictions…
Regularized models are often sensitive to the scales of the features in the data and it has therefore become standard practice to normalize (center and scale) the features before fitting the model. But there are many different ways to…
Inference for the parameters indexing generalised linear models is routinely based on the assumption that the model is correct and a priori specified. This is unsatisfactory because the chosen model is usually the result of a data-adaptive…