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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…

Machine Learning · Statistics 2011-12-30 Jian Huang , Cun-Hui Zhang

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

Optimization and Control · Mathematics 2019-05-27 Michael R. Metel , Akiko Takeda

Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…

Signal Processing · Electrical Eng. & Systems 2019-02-27 Marc Castella , Jean-Christophe Pesquet , Arthur Marmin

This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…

Statistics Theory · Mathematics 2020-07-28 Jose Blanchet , Peter W. Glynn , Jun Yan , Zhengqing Zhou

We propose MC+, a fast, continuous, nearly unbiased and accurate method of penalized variable selection in high-dimensional linear regression. The LASSO is fast and continuous, but biased. The bias of the LASSO may prevent consistent…

Statistics Theory · Mathematics 2010-02-26 Cun-Hui Zhang

In this paper, we consider the sparse least squares regression problem with probabilistic simplex constraint. Due to the probabilistic simplex constraint, one could not apply the L1 regularization to the considered regression model. To find…

Optimization and Control · Mathematics 2021-12-28 Guiyun Xiao , Zheng-Jian Bai

Sparse linear regression is a fundamental tool in data analysis. However, traditional approaches often fall short when covariates exhibit structure or arise from heterogeneous sources. In biomedical applications, covariates may stem from…

Machine Learning · Statistics 2026-05-19 William R. P. Denault

Translating machine learning algorithms into clinical applications requires addressing challenges related to interpretability, such as accounting for the effect of confounding variables (or metadata). Confounding variables affect the…

Machine Learning · Computer Science 2022-07-12 Anthony Vento , Qingyu Zhao , Robert Paul , Kilian M. Pohl , Ehsan Adeli

The simultaneous estimation of multiple unknown parameters lies at heart of a broad class of important problems across science and technology. Currently, the state-of-the-art performance in the such problems is achieved by nonparametric…

Statistics Theory · Mathematics 2023-05-30 Alton Barbehenn , Sihai Dave Zhao

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…

Optimization and Control · Mathematics 2025-05-30 Jun Fan , Ailing Yan , Xianchao Xiu , Wanquan Liu

In exact sparse optimization problems on Rd (also known as sparsity constrained problems), one looks for solution that have few nonzero components. In this paper, we consider problems where sparsity is exactly measured either by the…

Optimization and Control · Mathematics 2019-02-14 Jean-Philippe Chancelier , Michel De Lara , Ponts Paristech

Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better…

Machine Learning · Statistics 2023-05-25 Insung Kong , Dongyoon Yang , Jongjin Lee , Ilsang Ohn , Gyuseung Baek , Yongdai Kim

We introduce a parameterization method called Neural Bayes which allows computing statistical quantities that are in general difficult to compute and opens avenues for formulating new objectives for unsupervised representation learning.…

Machine Learning · Statistics 2020-02-24 Devansh Arpit , Huan Wang , Caiming Xiong , Richard Socher , Yoshua Bengio

Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…

Methodology · Statistics 2010-08-04 Xiwen Ma , Bin Dai , Ronald Klein , Barbara E. K. Klein , Kristine E. Lee , Grace Wahba

We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with $O(n^2)$ linear constraints ($n$ being the sample size), is difficult to…

Computation · Statistics 2015-09-29 Rahul Mazumder , Arkopal Choudhury , Garud Iyengar , Bodhisattva Sen

We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably…

Methodology · Statistics 2010-12-24 Yilun Chen , Yuantao Gu , Alfred O. Hero

Least squares fitting is in general not useful for high-dimensional linear models, in which the number of predictors is of the same or even larger order of magnitude than the number of samples. Theory developed in recent years has coined a…

Statistics Theory · Mathematics 2014-02-13 Martin Slawski , Matthias Hein

Mixed-effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures. In this article, we study an approach to the nonparametric estimation of mixed-effect models. We consider models with…

Statistics Theory · Mathematics 2007-06-13 Chong Gu , Ping Ma

We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…

Optimization and Control · Mathematics 2023-05-12 Duy-Nhat Phan , Sedi Bartz , Nilabja Guha , Hung M. Phan

In this report we review memory-based meta-learning as a tool for building sample-efficient strategies that learn from past experience to adapt to any task within a target class. Our goal is to equip the reader with the conceptual…