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We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

Methodology · Statistics 2019-09-09 Alexandre Belloni , Abhishek Kaul , Mathieu Rosenbaum

The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent disturbances given by a general square integrable semimartingale with unknown distribution. An example of such a…

Statistics Theory · Mathematics 2010-10-20 Victor Konev , Serguei Pergamenchtchikov

We consider a finite impulse response system with centered independent sub-Gaussian design covariates and noise components that are not necessarily identically distributed. We derive non-asymptotic near-optimal estimation and prediction…

Statistics Theory · Mathematics 2019-12-02 Boualem Djehiche , Othmane Mazhar , Cristian R. Rojas

In this paper, we consider the nonparametric regression problem with multivariate predictors. We provide a characterization of the degrees of freedom and divergence for estimators of the unknown regression function, which are obtained as…

Statistics Theory · Mathematics 2018-10-09 Xi Chen , Qihang Lin , Bodhisattva Sen

We study the least squares regression function estimator over the class of real-valued functions on $[0,1]^d$ that are increasing in each coordinate. For uniformly bounded signals and with a fixed, cubic lattice design, we establish that…

Statistics Theory · Mathematics 2017-09-01 Qiyang Han , Tengyao Wang , Sabyasachi Chatterjee , Richard J. Samworth

We study derivative-free methods for policy optimization over the class of linear policies. We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving…

Machine Learning · Computer Science 2020-05-19 Dhruv Malik , Ashwin Pananjady , Kush Bhatia , Koulik Khamaru , Peter L. Bartlett , Martin J. Wainwright

This paper gives two theoretical results on estimating low-rank parameter matrices for linear models with multivariate responses. We first focus on robust parameter estimation of low-rank multi-task learning with heavy-tailed data and…

Statistics Theory · Mathematics 2023-05-24 Kangqiang Li , Yuxuan Wang

We investigate how to improve efficiency using regression adjustments with covariates in covariate-adaptive randomizations (CARs) with imperfect subject compliance. Our regression-adjusted estimators, which are based on the doubly robust…

Econometrics · Economics 2023-06-19 Liang Jiang , Oliver B. Linton , Haihan Tang , Yichong Zhang

We consider (robust) inference in the context of a factor model for tensor-valued sequences. We study the consistency of the estimated common factors and loadings space when using estimators based on minimising quadratic loss functions.…

Methodology · Statistics 2023-08-29 Matteo Barigozzi , Yong He , Lingxiao Li , Lorenzo Trapani

We study (constrained) least-squares regression as well as multiple response least-squares regression and ask the question of whether a subset of the data, a coreset, suffices to compute a good approximate solution to the regression. We…

Data Structures and Algorithms · Computer Science 2016-11-18 Christos Boutsidis , Petros Drineas , Malik Magdon-Ismail

We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…

Machine Learning · Statistics 2016-04-15 Gilles Blanchard , Nicole Mücke

We study the so-called distributed two-time-scale gradient method for solving convex optimization problems over a network of agents when the communication bandwidth between the nodes is limited, and so information that is exchanged between…

Systems and Control · Electrical Eng. & Systems 2021-06-01 Marcos M. Vasconcelos , Thinh T. Doan , Urbashi Mitra

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 study the problem of learning adversarially robust halfspaces in the distribution-independent setting. In the realizable setting, we provide necessary and sufficient conditions on the adversarial perturbation sets under which halfspaces…

Machine Learning · Computer Science 2020-05-18 Omar Montasser , Surbhi Goel , Ilias Diakonikolas , Nathan Srebro

A method is proposed to generate an optimal fit of a number of connected linear trend segments onto time-series data. To be able to efficiently handle many lines, the method employs a stochastic search procedure to determine optimal…

Quantitative Methods · Quantitative Biology 2017-04-11 Myrl G. Marmarelis

With the explosion of massive, widely available unlabeled data in the past years, finding label and time efficient, robust learning algorithms has become ever more important in theory and in practice. We study the paradigm of active…

Machine Learning · Computer Science 2020-01-17 Max Hopkins , Daniel Kane , Shachar Lovett , Gaurav Mahajan

We give the first polynomial time and sample $(\epsilon, \delta)$-differentially private (DP) algorithm to estimate the mean, covariance and higher moments in the presence of a constant fraction of adversarial outliers. Our algorithm…

Machine Learning · Statistics 2021-12-08 Pravesh K. Kothari , Pasin Manurangsi , Ameya Velingker

In this paper, we study the problem of sparse mean estimation under adversarial corruptions, where the goal is to estimate the $k$-sparse mean of a heavy-tailed distribution from samples contaminated by adversarial noise. Existing methods…

Machine Learning · Computer Science 2025-08-26 Jianhao Ma , Rui Ray Chen , Yinghui He , Salar Fattahi , Wei Hu

We consider the estimation of a bounded regression function with nonparametric heteroscedastic noise and random design. We study the true and empirical excess risks of the least-squares estimator on finite-dimensional vector spaces. We give…

Statistics Theory · Mathematics 2015-06-29 Adrien Saumard

In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…

Statistics Theory · Mathematics 2025-12-05 Kangqiang Li , Bingqi Liu , Yang Yang , Li Wang