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Multivariate regression model is a natural generalization of the classical univari- ate regression model for fitting multiple responses. In this paper, we propose a high- dimensional multivariate conditional regression model for…

We study the bias of classical quantile regression and instrumental variable quantile regression estimators. While being asymptotically first-order unbiased, these estimators can have non-negligible second-order biases. We derive a…

Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian…

Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…

Measurement error arises through a variety of mechanisms. A rich literature exists on the bias introduced by covariate measurement error and on methods of analysis to address this bias. By comparison, less attention has been given to errors…

The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…

The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…

We investigate the choice of tuning parameters for a Bayesian multi-level group lasso model developed for the joint analysis of neuroimaging and genetic data. The regression model we consider relates multivariate phenotypes consisting of…

We consider the problem of variable selection in Bayesian multivariate linear regression models, involving multiple response and predictor variables, under multivariate normal errors. In the absence of a known covariance structure,…

Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the…

We consider distributed optimization problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We develop unbiased parameter averaging methods for randomized second order optimization…

Algorithmic Bias can be due to bias in the training data or issues with the algorithm itself. These algorithmic issues typically relate to problems with model capacity and regularisation. This underestimation bias may arise because the…

Parametric Bayesian modeling offers a powerful and flexible toolbox for machine learning. Yet the model, however detailed, may still be wrong, and this can make inferences untrustworthy. In this paper we introduce a new class of…

This paper presents a general framework for the estimation of regression models with circular covariates, where the conditional distribution of the response given the covariate can be specified through a parametric model. The estimation of…

In model development, model calibration and validation play complementary roles toward learning reliable models. In this article, we expand the Bayesian Validation Metric framework to a general calibration and validation framework by…

We develop a general estimation and inference procedure for the common parameters in linear panel data regression models with nonparametric two-way specification of unobserved heterogeneity. The procedure takes as input any first-step…

The bias-variance trade-off is a central concept in supervised learning. In classical statistics, increasing the complexity of a model (e.g., number of parameters) reduces bias but also increases variance. Until recently, it was commonly…

The generalization capacity of various machine learning models exhibits different phenomena in the under- and over-parameterized regimes. In this paper, we focus on regression models such as feature regression and kernel regression and…

Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…

Univariate and multivariate general linear regression models, subject to linear inequality constraints, arise in many scientific applications. The linear inequality restrictions on model parameters are often available from phenomenological…