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A multi-fidelity regression model is proposed for combining multiple datasets with different fidelities, particularly abundant low-fidelity data and scarce high-fidelity observations. The model builds upon recent multi-fidelity frameworks…

Gaussian Process Regression and Kernel Ridge Regression are popular nonparametric regression approaches. Unfortunately, they suffer from high computational complexity rendering them inapplicable to the modern massive datasets. To that end a…

Statistical and structural modeling represent two distinct approaches to data analysis. In this paper, we propose a set of novel methods for combining statistical and structural models for improved prediction and causal inference. Our first…

This paper introduces a novel framework for estimation and inference in penalized M-estimators applied to robust high-dimensional linear regression models. Traditional methods for high-dimensional statistical inference, which predominantly…

Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…

Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…

Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of…

We propose a statistical inference framework for the component-wise functional gradient descent algorithm (CFGD) under normality assumption for model errors, also known as $L_2$-Boosting. The CFGD is one of the most versatile tools to…

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…

Combining additive models and neural networks allows to broaden the scope of statistical regression and extend deep learning-based approaches by interpretable structured additive predictors at the same time. Existing attempts uniting the…

The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…

Regression, unlike classification, has lacked a comprehensive and effective approach to deal with cost-sensitive problems by the reuse (and not a re-training) of general regression models. In this paper, a wide variety of cost-sensitive…

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…

Among semiparametric regression models, partially linear additive models provide a useful tool to include additive nonparametric components as well as a parametric component, when explaining the relationship between the response and a set…

The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…

We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions…

The Neural Contextual Reinforcement Framework introduces an innovative approach to enhancing the logical coherence and structural consistency of text generated by large language models. Leveraging reinforcement learning principles, the…

Regression analysis has always been a hot research topic in statistics. We propose a very flexible semi-parametric regression model called Elliptical Copula Regression (ECR) model, which covers a large class of linear and nonlinear…

Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic…

Algorithmic recourse provides individuals who receive undesirable outcomes from machine learning systems with minimum-cost improvements to achieve a desirable outcome. However, machine learning models often get updated, so the recourse may…