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Several regularization methods have been considered over the last decade for sparse high-dimensional linear regression models, but the most common ones use the least square (quadratic) or likelihood loss and hence are not robust against…

Modern machine learning methods have recently demonstrated remarkable capability to generalize under task shift, where latent knowledge is transferred to a different, often more difficult, task under a similar data distribution. We…

A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows…

Robots rely on visual relocalization to estimate their pose from camera images when they lose track. One of the challenges in visual relocalization is repetitive structures in the operation environment of the robot. This calls for…

One of the main open problems in the qualitative theory of real planar differential systems is the study of limit cycles. In this article, we present an algorithmic approach for detecting how many limit cycles can bifurcate from the…

This paper introduces a new type of regression methodology named as Convex-Area-Wise Linear Regression(CALR), which separates given datasets by disjoint convex areas and fits different linear regression models for different areas. This…

Generalized linear models and the quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. Nonparametric methods need no explicit parametric specification, and the…

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

In this contribution, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such…

Pseudo-labeling is a commonly used paradigm in semi-supervised learning, yet its application to semi-supervised regression (SSR) remains relatively under-explored. Unlike classification, where pseudo-labels are discrete and confidence-based…

This paper proposes a Lasso-type estimator for a high-dimensional sparse parameter identified by a single index conditional moment restriction (CMR). In addition to this parameter, the moment function can also depend on a nuisance function,…

Semi-supervised learning by self-training heavily relies on pseudo-label selection (PLS). The selection often depends on the initial model fit on labeled data. Early overfitting might thus be propagated to the final model by selecting…

Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…

Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid…

We prove several new results about bounded uniform and small-bias distributions. A main message is that, small-bias, even perturbed with noise, does not fool several classes of tests better than bounded uniformity. We prove this for…

We propose a novel sensitivity analysis framework for linear estimators with identification failures that can be viewed as seeing the wrong outcome distribution. Our approach measures the degree of identification failure through the change…

Transfer learning aims to improve performance on a target task by leveraging information from related source tasks. We propose a nonparametric regression transfer learning framework that explicitly models heterogeneity in the source-target…

In this paper we propose a semi-parametric Bayesian Generalized Least Squares estimator. In a generic setting where each error is a vector, the parametric Generalized Least Square estimator maintains the assumption that each error vector…

This paper considers the problem of estimation in the generalized semiparametric model for longitudinal data when the number of parameters diverges with the sample size. A penalization type of generalized estimating equation method is…

Foundation models have achieved remarkable success across diverse machine-learning domains through large-scale pretraining on large, diverse datasets. However, pretraining on such datasets introduces significant challenges due to…