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We investigate various stochastic bandit problems in the presence of adversarial corruptions. A seminal work for this problem is the BARBAR~\cite{gupta2019better} algorithm, which achieves both robustness and efficiency. However, it suffers…

Machine Learning · Computer Science 2026-01-05 Zicheng Hu , Cheng Chen

We consider a data corruption scenario in the classical $k$ Nearest Neighbors ($k$-NN) algorithm, that is, the testing data are randomly perturbed. Under such a scenario, the impact of corruption level on the asymptotic regret is carefully…

Machine Learning · Statistics 2020-02-14 Yue Xing , Qifan Song , Guang Cheng

We study quantile trend filtering, a recently proposed method for nonparametric quantile regression with the goal of generalizing existing risk bounds known for the usual trend filtering estimators which perform mean regression. We study…

Statistics Theory · Mathematics 2021-08-31 Oscar Hernan Madrid Padilla , Sabyasachi Chatterjee

The Bregman-Kaczmarz method is an iterative method which can solve strongly convex problems with linear constraints and uses only one or a selected number of rows of the system matrix in each iteration, thereby making it amenable for…

Optimization and Control · Mathematics 2023-07-31 Dirk A. Lorenz , Maximilian Winkler

The nonlinear Kaczmarz method was recently proposed to solve the system of nonlinear equations. In this paper, we first discuss two greedy selection rules, i.e., the maximum residual and maximum distance rules, for the nonlinear Kaczmarz…

Numerical Analysis · Mathematics 2022-09-14 Yanjun Zhang , Hanyu Li , Ling Tang

This paper introduces an innovative error feedback framework designed to mitigate quantization noise in distributed graph filtering, where communications are constrained to quantized messages. It comes from error spectrum shaping techniques…

Machine Learning · Computer Science 2026-05-12 Xue Xian Zheng , Weihang Liu , Xin Lou , Stefan Vlaski , Tareq Al-Naffouri

We study Gaussian sparse estimation tasks in Huber's contamination model with a focus on mean estimation, PCA, and linear regression. For each of these tasks, we give the first sample and computationally efficient robust estimators with…

Machine Learning · Computer Science 2024-03-18 Ilias Diakonikolas , Daniel M. Kane , Sushrut Karmalkar , Ankit Pensia , Thanasis Pittas

In this paper, based on an optimization problem, a sketch-and-project method for solving the linear matrix equation AXB = C is proposed. We provide a thorough convergence analysis for the new method and derive a lower bound on the…

Numerical Analysis · Mathematics 2023-06-07 Wendi Bao , Zhiwei Guo , Weiguo Li , Ying Lv , Jichao Wang

Conformalized Quantile Regression (CQR) is a recently proposed method for constructing prediction intervals for a response $Y$ given covariates $X$, without making distributional assumptions. However, existing constructions of CQR can be…

Methodology · Statistics 2024-05-16 Raphael Rossellini , Rina Foygel Barber , Rebecca Willett

The Kaczmarz method (KZ) and its variants, which are types of stochastic gradient descent (SGD) methods, have been extensively studied due to their simplicity and efficiency in solving linear equation systems. The iterative thresholding…

Machine Learning · Statistics 2023-04-21 Halyun Jeong , Deanna Needell

Censored quantile regression (CQR) has become a valuable tool to study the heterogeneous association between a possibly censored outcome and a set of covariates, yet computation and statistical inference for CQR have remained a challenge…

Statistics Theory · Mathematics 2022-10-25 Xuming He , Xiaoou Pan , Kean Ming Tan , Wen-Xin Zhou

The scalable adaptive cubic regularization method ($\mathrm{ARC_{q}K}$: Dussault et al. in Math. Program. Ser. A 207(1-2): 191-225, 2024) has been recently proposed for unconstrained optimization. It has excellent convergence properties,…

Optimization and Control · Mathematics 2026-03-17 Yonggang Pei , Yubing Lin , Shuai Shao , Mauricio Silva Louzeiro , Detong Zhu

Randomized iterative algorithms, such as the randomized Kaczmarz method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our present work leverages the insights…

In this paper, we study the problem of estimating latent variable models with arbitrarily corrupted samples in high dimensional space ({\em i.e.,} $d\gg n$) where the underlying parameter is assumed to be sparse. Specifically, we propose a…

Machine Learning · Statistics 2020-10-20 Di Wang , Xiangyu Guo , Shi Li , Jinhui Xu

We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $\vert x \rangle$ that is proportional to the solution of the system of linear equations $A…

Quantum Physics · Physics 2019-02-20 Yigit Subasi , Rolando D. Somma , Davide Orsucci

We propose two new methods to address the weak scaling problems of KRR: the Balanced KRR (BKRR) and K-means KRR (KKRR). These methods consider alternative ways to partition the input dataset into p different parts, generating p different…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-05-03 Yang You , James Demmel , Cho-Jui Hsieh , Richard Vuduc

In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…

Quantum Physics · Physics 2024-11-26 Hyunju Lee , Kyungtaek Jun

With a quite different way to determine the working rows, we propose a novel greedy Kaczmarz method for solving consistent linear systems. Convergence analysis of the new method is provided. Numerical experiments show that, for the same…

Numerical Analysis · Mathematics 2020-04-07 Hanyu Li , Yanjun Zhang

In this paper, we consider a novel two-dimensional randomized Kaczmarz method and its improved version with simple random sampling, which chooses two active rows with probability proportional to the square of their cross-product-like…

Numerical Analysis · Mathematics 2025-06-27 Tao Li , Meng-Long Xiao , Xin-Fang Zhang

The multi-step inertial randomized Kaczmarz (MIRK) method is an iterative method for solving large-scale linear systems. In this paper, we enhance the MIRK method by incorporating the greedy probability criterion, coupled with the…

Numerical Analysis · Mathematics 2024-10-10 Yansheng Su , Deren Han , Yun Zeng , Jiaxin Xie