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Related papers: Adaptive robust estimation in sparse vector model

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We study a seemingly unexpected and relatively less understood overfitting aspect of a fundamental tool in sparse linear modeling - best subset selection, which minimizes the residual sum of squares subject to a constraint on the number of…

Methodology · Statistics 2022-01-11 Rahul Mazumder , Peter Radchenko , Antoine Dedieu

Many parametric statistical models are not properly normalised and only specified up to an intractable partition function, which renders parameter estimation difficult. Examples of unnormalised models are Gibbs distributions, Markov random…

Machine Learning · Statistics 2018-06-12 Ciwan Ceylan , Michael U. Gutmann

We derive improved regression and classification rates for support vector machines using Gaussian kernels under the assumption that the data has some low-dimensional intrinsic structure that is described by the box-counting dimension. Under…

Statistics Theory · Mathematics 2021-04-08 Thomas Hamm , Ingo Steinwart

We study estimation and testing in the Poisson regression model with noisy high dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a…

Statistics Theory · Mathematics 2023-01-03 Fei Jiang , Yeqing Zhou , Jianxuan Liu , Yanyuan Ma

We study the distribution of hard-, soft-, and adaptive soft-thresholding estimators within a linear regression model where the number of parameters k can depend on sample size n and may diverge with n. In addition to the case of known…

Statistics Theory · Mathematics 2012-01-04 Benedikt M. Pötscher , Ulrike Schneider

In this paper, a new method for the separation of noise categories based on Four-Wave Mixing is presented. The theoretical analysis is grounded in the Gaussian Noise model and verified by split step simulations. The noise categories react…

Systems and Control · Electrical Eng. & Systems 2022-09-14 F. J. Vaquero-Caballero , D. J. Ives , S. J. Savory

We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured…

Statistics Theory · Mathematics 2022-05-10 T. Tony Cai , Anru R. Zhang , Yuchen Zhou

This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise…

Statistics Theory · Mathematics 2015-06-11 T. Tony Cai , Xiaodong Li , Zongming Ma

We consider the problem of estimating a sparse linear regression vector $\beta^*$ under a gaussian noise model, for the purpose of both prediction and model selection. We assume that prior knowledge is available on the sparsity pattern,…

Statistics Theory · Mathematics 2012-08-21 Karim Lounici , Massimiliano Pontil , Alexandre B. Tsybakov , Sara van de Geer

We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure,…

Statistics Theory · Mathematics 2016-05-03 Julyan Arbel , Ghislaine Gayraud , Judith Rousseau

We consider a semiparametric convolution model. We observe random variables having a distribution given by the convolution of some unknown density $f$ and some partially known noise density $g$. In this work, $g$ is assumed exponentially…

Statistics Theory · Mathematics 2008-10-03 Cristina Butucea , Catherine Matias , Christophe Pouet

Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…

Methodology · Statistics 2024-03-11 Ryan Thompson , Farshid Vahid

We consider a problem of estimating a sparse group of sparse normal mean vectors. The proposed approach is based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their…

Statistics Theory · Mathematics 2012-03-02 Felix Abramovich , Vadim Grinshtein

Multiple-stage adaptive architectures are conceived to face with the problem of target detection buried in noise, clutter, and intentional interference. First, a scenario where the radar system is under the electronic attack of noise-like…

Signal Processing · Electrical Eng. & Systems 2020-04-28 Linjie Yan , Pia Addabbo , Chengpeng Hao , Danilo Orlando , Alfonso Farina

This paper introduces a noise-tolerant computing method for over-the-air computation (AirComp) aimed at weighted averaging, which is critical in various Internet of Things (IoT) applications such as environmental monitoring. Traditional…

Signal Processing · Electrical Eng. & Systems 2025-04-23 Koya Sato , Koji Ishibashi

While neural networks have made significant strides in many AI tasks, they remain vulnerable to a range of noise types, including natural corruptions, adversarial noise, and low-resolution artifacts. Many existing approaches focus on…

Computer Vision and Pattern Recognition · Computer Science 2024-09-30 Zhiling Zhou , Zirui Liu , Chengming Xu , Yanwei Fu , Xinwei Sun

We construct efficient robust truncated sequential estimators for the pointwise estimation problem in nonparametric autoregression models with smooth coefficients. For Gaussian models we propose an adaptive procedure based on the…

Statistics Theory · Mathematics 2013-04-18 Ouerdia Arkoun , Serguei Pergamenchtchikov

Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…

Statistics Theory · Mathematics 2021-08-10 Ilsang Ohn , Yongdai Kim

The paper deals with the non-parametric estimation in the regression with the multiplicative noise. Using the local polynomial fitting and the bayesian approach, we construct the minimax on isotropic H\"older class estimator. Next applying…

Statistics Theory · Mathematics 2012-07-24 M. Chichignoud

We consider the linear inverse problem of estimating an unknown signal $f$ from noisy measurements on $Kf$ where the linear operator $K$ admits a wavelet-vaguelette decomposition (WVD). We formulate the problem in the Gaussian sequence…

Statistics Theory · Mathematics 2014-08-25 Iain M. Johnstone , Debashis Paul