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Being robust to the presence of outliers is crucial for applying clustering algorithms in practice. In the $\textit{robust $k$-Means}$ problem (i.e., $k$-Means with outliers), the goal is to remove $z$ outliers and minimize the $k$-Means…

Machine Learning · Computer Science 2026-05-11 Tianle Jiang , Yufa Zhou

We consider offline Imitation Learning from corrupted demonstrations where a constant fraction of data can be noise or even arbitrary outliers. Classical approaches such as Behavior Cloning assumes that demonstrations are collected by an…

Machine Learning · Computer Science 2022-02-01 Liu Liu , Ziyang Tang , Lanqing Li , Dijun Luo

Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…

Statistics Theory · Mathematics 2014-10-09 Jianqing Fan , Quefeng Li , Yuyan Wang

Learning from data in the presence of outliers is a fundamental problem in statistics. Until recently, no computationally efficient algorithms were known to compute the mean of a high dimensional distribution under natural assumptions in…

Data Structures and Algorithms · Computer Science 2021-01-22 Yeshwanth Cherapanamjeri , Sidhanth Mohanty , Morris Yau

Fully robust versions of the elastic net estimator are introduced for linear and logistic regression. The algorithms to compute the estimators are based on the idea of repeatedly applying the non-robust classical estimators to data subsets…

Methodology · Statistics 2017-03-16 Fatma Sevinc Kurnaz , Irene Hoffmann , Peter Filzmoser

We study the problem of estimating the means of well-separated mixtures when an adversary may add arbitrary outliers. While strong guarantees are available when the outlier fraction is significantly smaller than the minimum mixing weight,…

Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…

Statistics Theory · Mathematics 2025-05-07 Alejandro Cholaquidis , Ricardo Fraiman , Leonardo Moreno , Gonzalo Perera

We study the out-of-sample properties of robust empirical optimization problems with smooth $\phi$-divergence penalties and smooth concave objective functions, and develop a theory for data-driven calibration of the non-negative "robustness…

Machine Learning · Statistics 2020-05-20 Jun-Ya Gotoh , Michael Jong Kim , Andrew E. B. Lim

In real world, our datasets often contain outliers. Moreover, the outliers can seriously affect the final machine learning result. Most existing algorithms for handling outliers take high time complexities (e.g. quadratic or cubic…

Computational Geometry · Computer Science 2020-02-28 Hu Ding , Zixiu Wang

Structured statistical estimation problems are often solved by Conditional Gradient (CG) type methods to avoid the computationally expensive projection operation. However, the existing CG type methods are not robust to data corruption. To…

Machine Learning · Computer Science 2020-07-08 Jiacheng Zhuo , Liu Liu , Constantine Caramanis

In statistical learning and analysis from shared data, which is increasingly widely adopted in platforms such as federated learning and meta-learning, there are two major concerns: privacy and robustness. Each participating individual…

Machine Learning · Computer Science 2021-11-25 Xiyang Liu , Weihao Kong , Sham Kakade , Sewoong Oh

In many applications, when building linear regression models, it is important to account for the presence of outliers, i.e., corrupted input data points. Such problems can be formulated as mixed-integer optimization problems involving cubic…

Optimization and Control · Mathematics 2023-07-13 Andrés Gómez , José Neto

ML-estimation based on mixtures of Normal distributions is a widely used tool for cluster analysis. However, a single outlier can make the parameter estimation of at least one of the mixture components break down. Among others, the…

Statistics Theory · Mathematics 2007-06-13 Christian Hennig

We consider the robust multi-dimensional scaling (RMDS) problem in this paper. The goal is to localize point locations from pairwise distances that may be corrupted by outliers. Inspired by classic MDS theories, and nonconvex works for the…

Machine Learning · Statistics 2025-01-07 Tong Deng , Tianming Wang

We study the fundamental problems of Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination. Our main contribution is the design of the first sample near-optimal and almost linear-time…

Data Structures and Algorithms · Computer Science 2023-12-05 Ilias Diakonikolas , Daniel M. Kane , Ankit Pensia , Thanasis Pittas

We propose a robust elastic net (REN) model for high-dimensional sparse regression and give its performance guarantees (both the statistical error bound and the optimization bound). A simple idea of trimming the inner product is applied to…

Machine Learning · Computer Science 2016-05-03 Weiyang Liu , Rongmei Lin , Meng Yang

Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…

Methodology · Statistics 2018-10-17 Kei Hirose , Hiroki Masuda

Rare data in a large-scale database are called outliers that reveal significant information in the real world. The subspace-based outlier detection is regarded as a feasible approach in very high dimensional space. However, the outliers…

Artificial Intelligence · Computer Science 2014-05-06 Zhana Bao

Many estimation problems in robotics, computer vision, and learning require estimating unknown quantities in the face of outliers. Outliers are typically the result of incorrect data association or feature matching, and it is common to have…

Computer Vision and Pattern Recognition · Computer Science 2021-03-25 Jingnan Shi , Heng Yang , Luca Carlone

We study the problem of robust linear regression with response variable corruptions. We consider the oblivious adversary model, where the adversary corrupts a fraction of the responses in complete ignorance of the data. We provide a nearly…

Machine Learning · Computer Science 2019-03-21 Arun Sai Suggala , Kush Bhatia , Pradeep Ravikumar , Prateek Jain