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This paper presents a novel approach for pointwise estimation of multivariate density functions on known domains of arbitrary dimensions using nonparametric local polynomial estimators. Our method is highly flexible, as it applies to both…

Inference by means of mathematical modeling from a collection of observations remains a crucial tool for scientific discovery and is ubiquitous in application areas such as signal compression, imaging restoration, and supervised machine…

The Highly Adaptive Lasso (HAL) is a nonparametric regression method that achieves almost dimension-free convergence rates under minimal smoothness assumptions, but its implementation can be computationally prohibitive in high dimensions…

Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving…

Logistic regression involving high-dimensional covariates is a practically important problem. Often the goal is variable selection, i.e., determining which few of the many covariates are associated with the binary response. Unfortunately,…

The generalized outcome-adaptive lasso (GOAL) is a variable selection for high-dimensional causal inference proposed by Bald\'e et al. [2023, {\em Biometrics} {\bfseries 79(1)}, 514--520]. When the dimension is high, it is now well…

Computational reconstruction plays a vital role in computer vision and computational photography. Most of the conventional optimization and deep learning techniques explore local information for reconstruction. Recently, nonlocal low-rank…

Key science questions, such as galaxy distance estimation and weather forecasting, often require knowing the full predictive distribution of a target variable $y$ given complex inputs $\mathbf{x}$. Despite recent advances in machine…

Due to its low computational cost, Lasso is an attractive regularization method for high-dimensional statistical settings. In this paper, we consider multivariate counting processes depending on an unknown function parameter to be estimated…

Graphs and networks are common ways of depicting biological information. In biology, many different biological processes are represented by graphs, such as regulatory networks, metabolic pathways and protein--protein interaction networks.…

Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…

Linear regression is effective at identifying interpretable trends in a data set, but averages out potentially different effects on subgroups within data. We propose an iterative algorithm based on the randomized Kaczmarz (RK) method to…

Adaptive stochastic gradient methods such as AdaGrad have gained popularity in particular for training deep neural networks. The most commonly used and studied variant maintains a diagonal matrix approximation to second order information by…

Projection-free conditional gradient (CG) methods are the algorithms of choice for constrained optimization setups in which projections are often computationally prohibitive but linear optimization over the constraint set remains…

Stochastic optimization plays a crucial role in the advancement of deep learning technologies. Over the decades, significant effort has been dedicated to improving the training efficiency and robustness of deep neural networks, via various…

LASSO regularized logistic regression is particularly useful for its built-in feature selection, allowing coefficients to be removed from deployment and producing sparse solutions. Differentially private versions of LASSO logistic…

In this paper, we propose a novel variable selection approach in the framework of multivariate linear models taking into account the dependence that may exist between the responses. It consists in estimating beforehand the covariance matrix…

One of the main problems studied in statistics is the fitting of models. Ideally, we would like to explain a large dataset with as few parameters as possible. There have been numerous attempts at automatizing this process. Most notably, the…

Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with…

Multi-Objective Reinforcement Learning (MORL) is a generalization of traditional Reinforcement Learning (RL) that aims to optimize multiple, often conflicting objectives simultaneously rather than focusing on a single reward. This approach…