English
Related papers

Related papers: Efficient Algorithms for Outlier-Robust Regression

200 papers

We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…

Robust low-rank approximation under row-wise adversarial corruption can be achieved with a single pass, randomized procedure that detects and removes outlier rows by thresholding their projected norms. We propose a scalable, non-iterative…

Machine Learning · Computer Science 2025-04-04 Aidan Tiruvan

We revisit the problem of estimating the mean of a high-dimensional distribution in the presence of an $\varepsilon$-fraction of adversarial outliers. When $\varepsilon$ is at most some sufficiently small constant, previous works can…

Data Structures and Algorithms · Computer Science 2024-11-22 Hongjie Chen , Deepak Narayanan Sridharan , David Steurer

This work develops robust diffusion recursive least squares algorithms to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. The first algorithm minimizes an exponentially…

Machine Learning · Computer Science 2019-02-05 Y. Yu , H. Zhao , R. C. de Lamare , Y. Zakharov , L. Lu

This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with…

Machine Learning · Computer Science 2019-04-22 Fabien Lauer

We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first…

Optimization and Control · Mathematics 2016-02-25 Aymeric Dieuleveut , Nicolas Flammarion , Francis Bach

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

Machine Learning · Computer Science 2021-06-04 Quanming Yao , Hangsi Yang , En-Liang Hu , James Kwok

We study the algorithmic problem of sparse mean estimation in the presence of adversarial outliers. Specifically, the algorithm observes a \emph{corrupted} set of samples from $\mathcal{N}(\mu,\mathbf{I}_d)$, where the unknown mean $\mu \in…

Data Structures and Algorithms · Computer Science 2024-03-08 Ankit Pensia

In this work, we revisit the problem of estimating the mean and covariance of an unknown $d$-dimensional Gaussian distribution in the presence of an $\varepsilon$-fraction of adversarial outliers. The pioneering work of [DKK+16] gave a…

Data Structures and Algorithms · Computer Science 2021-10-25 Pravesh K. Kothari , Peter Manohar , Brian Hu Zhang

We adapt a manifold sampling algorithm for the nonsmooth, nonconvex formulations of learning that arise when imposing robustness to outliers present in the training data. We demonstrate the approach on objectives based on trimmed loss.…

Optimization and Control · Mathematics 2018-07-10 Matt Menickelly , Stefan M. Wild

Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…

Machine Learning · Statistics 2016-08-01 Abolfazl Hashemi , Haris Vikalo

Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in…

Machine Learning · Computer Science 2019-10-07 Manolis C. Tsakiris , Liangzu Peng , Aldo Conca , Laurent Kneip , Yuanming Shi , Hayoung Choi

This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least…

Machine Learning · Computer Science 2017-11-09 Daniel Hsu , Kevin Shi , Xiaorui Sun

We present a quantum algorithm for fitting a linear regression model to a given data set using the least squares approach. Different from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs…

Quantum Physics · Physics 2017-08-01 Guoming Wang

In this paper, we consider a generalized multivariate regression problem where the responses are monotonic functions of linear transformations of predictors. We propose a semi-parametric algorithm based on the ordering of the responses…

Machine Learning · Statistics 2016-02-22 Milad Kharratzadeh , Mark Coates

We study the following basic machine learning task: Given a fixed set of $d$-dimensional input points for a linear regression problem, we wish to predict a hidden response value for each of the points. We can only afford to attain the…

Machine Learning · Computer Science 2018-06-07 Michał Dereziński , Manfred K. Warmuth

Robust mean estimation is the problem of estimating the mean $\mu \in \mathbb{R}^d$ of a $d$-dimensional distribution $D$ from a list of independent samples, an $\epsilon$-fraction of which have been arbitrarily corrupted by a malicious…

Computational Complexity · Computer Science 2019-06-05 Samuel B. Hopkins , Jerry Li

This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…

Optimization and Control · Mathematics 2020-07-15 Jineng Ren , Jarvis Haupt

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

Data Structures and Algorithms · Computer Science 2023-05-29 Jonathan Kelner , Frederic Koehler , Raghu Meka , Dhruv Rohatgi

We give the first fully polynomial-time algorithm for learning halfspaces with respect to the uniform distribution on the hypercube in the presence of contamination, where an adversary may corrupt some fraction of examples and labels…

Data Structures and Algorithms · Computer Science 2025-11-11 Gautam Chandrasekaran , Adam R. Klivans , Konstantinos Stavropoulos , Arsen Vasilyan