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Covariate shift occurs prevalently in practice, where the input distributions of the source and target data are substantially different. Despite its practical importance in various learning problems, most of the existing methods only focus…
Sparse penalized quantile regression provides an effective framework for variable selection and robust estimation in high-dimensional data analysis. When ex planatory variables are organized into groups, achieving sparsity both within and…
Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…
Censored quantile regression has emerged as a prominent alternative to classical Cox's proportional hazards model or accelerated failure time model in both theoretical and applied statistics. While quantile regression has been extensively…
Hybrid variational quantum algorithms are promising for solving practical problems, such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers.…
We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…
Quantile crossing is a common phenomenon in shape constrained nonparametric quantile regression. A recent study by Wang et al. (2014) has proposed to address this problem by imposing non-crossing constraints to convex quantile regression.…
In this article, we propose a penalized clustering method for large scale data with multiple covariates through a functional data approach. In the proposed method, responses and covariates are linked together through nonparametric…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
Nowadays, several data analysis problems require for complexity reduction, mainly meaning that they target at removing the non-influential covariates from the model and at delivering a sparse model. When categorical covariates are present,…
In reinforcement learning (RL), Q-learning is a fundamental algorithm whose convergence is guaranteed in the tabular setting. However, this convergence guarantee does not hold under linear function approximation. To overcome this…
In multivariate regression, when covariates are numerous, it is often reasonable to assume that only a small number of them has predictive information. In some medical applications for instance, it is believed that only a few genes out of…
Quantile Regression (QR) can be used to estimate aleatoric uncertainty in deep neural networks and can generate prediction intervals. Quantifying uncertainty is particularly important in critical applications such as clinical diagnosis,…
One of the most important problems in regression-based error model is modeling the complex representation error caused by various corruptions and environment changes in images. For example, in robust face recognition, images are often…
Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications,…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…
The computational prediction algorithm of neural network, or deep learning, has drawn much attention recently in statistics as well as in image recognition and natural language processing. Particularly in statistical application for…
Coefficient estimation and variable selection in multiple linear regression is routinely done in the (penalized) least squares (LS) framework. The concept of model selection oracle introduced by Fan and Li [J. Amer. Statist. Assoc. 96…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…