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Minimax problems are notoriously challenging to optimize. However, we present that the two-timescale extragradient method can be a viable solution. By utilizing dynamical systems theory, we show that it converges to points that satisfy the…

Optimization and Control · Mathematics 2024-04-23 Jiseok Chae , Kyuwon Kim , Donghwan Kim

We prove lower bounds on the complexity of finding $\epsilon$-stationary points (points $x$ such that $\|\nabla f(x)\| \le \epsilon$) of smooth, high-dimensional, and potentially non-convex functions $f$. We consider oracle-based complexity…

Optimization and Control · Mathematics 2019-08-16 Yair Carmon , John C. Duchi , Oliver Hinder , Aaron Sidford

In this paper, we consider the setting of piecewise i.i.d. bandits under a safety constraint. In this piecewise i.i.d. setting, there exists a finite number of changepoints where the mean of some or all arms change simultaneously. We…

Machine Learning · Computer Science 2022-05-30 Subhojyoti Mukherjee

Generalization error (also known as the out-of-sample error) measures how well the hypothesis learned from training data generalizes to previously unseen data. Proving tight generalization error bounds is a central question in statistical…

Machine Learning · Computer Science 2020-03-03 Jian Li , Xuanyuan Luo , Mingda Qiao

In this paper, we aim to give a theoretical approximation for the penalty level of $\ell_{1}$-regularization problems. This can save much time in practice compared with the traditional methods, such as cross-validation. To achieve this…

Statistics Theory · Mathematics 2020-02-19 Fang Xie

This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise…

Methodology · Statistics 2023-10-09 Zifeng Zhao , Ting Fung Ma , Wai Leong Ng , Chun Yip Yau

This paper considers weak Galerkin finite element approximations for a quasistatic Maxwell viscoelastic model. The spatial discretization uses piecewise polynomials of degree $k \ (k\geq 1)$ for the stress approximation, degree $k+1$ for…

Numerical Analysis · Mathematics 2022-02-22 Jihong Xiao , Zimo Zhu , Xiaoping Xie

The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of…

Statistics Theory · Mathematics 2024-07-26 Randolf Altmeyer , Anton Tiepner , Martin Wahl

The investigation of samples with a spatial resolution in the nanometer range relies on the precise and stable positioning of the sample. Due to inherent mechanical instabilities of typical sample stages in optical microscopes, it is…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-06-07 Marcel Leutenegger , Michael Weber

We introduce a novel dynamic learning-rate scheduling scheme grounded in theory with the goal of simplifying the manual and time-consuming tuning of schedules in practice. Our approach is based on estimating the locally-optimal stepsize,…

Machine Learning · Computer Science 2023-11-27 Gilad Yehudai , Alon Cohen , Amit Daniely , Yoel Drori , Tomer Koren , Mariano Schain

Gaussian mixture models are widely used to study clustering problems. These model-based clustering methods require an accurate estimation of the unknown data density by Gaussian mixtures. In Maugis and Michel (2009), a penalized maximum…

Statistics Theory · Mathematics 2015-03-19 Maugis Cathy , Michel Bertrand

This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…

Systems and Control · Computer Science 2018-07-27 Chiara Ravazzi , Nelson P. K. Chan , Paolo Frasca

Probabilistic encoding introduces Gaussian noise into neural networks, enabling a smooth transition from deterministic to uncertain states and enhancing generalization ability. However, the randomness of Gaussian noise distorts point-based…

Machine Learning · Computer Science 2025-07-24 Pengjiu Xia , Yidian Huang , Wenchao Wei , Yuwen Tan

We aim at analyzing geostatistical and areal data observed over irregularly shaped spatial domains and having a distribution within the exponential family. We propose a generalized additive model that allows to account for spatially-varying…

Methodology · Statistics 2016-04-22 Matthieu Wilhelm , Laura M. Sangalli

We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve…

Data Structures and Algorithms · Computer Science 2017-11-07 Ilias Diakonikolas , Gautam Kamath , Daniel M. Kane , Jerry Li , Ankur Moitra , Alistair Stewart

We analyze convergence of gradient-descent methods on Riemannian manifolds. In particular, we study randomization of Riemannian gradient algorithms for minimizing smooth cost functions (of Morse-Bott type). We prove that randomized gradient…

Optimization and Control · Mathematics 2025-07-08 Emanuel Malvetti , Christian Arenz , Gunther Dirr , Thomas Schulte-Herbrüggen

Analysis of low-degree polynomial algorithms is a powerful, newly-popular method for predicting computational thresholds in hypothesis testing problems. One limitation of current techniques for this analysis is their restriction to…

Statistics Theory · Mathematics 2020-11-10 Dmitriy Kunisky

We consider the problem of constructing confidence intervals for the locations of change points in a high-dimensional mean shift model. To that end, we develop a locally refitted least squares estimator and obtain component-wise and…

Methodology · Statistics 2021-07-21 Abhishek Kaul , George Michailidis

A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…

Optimization and Control · Mathematics 2018-03-12 Craig Wilson , Venugopal Veeravalli , Angelia Nedich

We consider signal source localization from range-difference measurements. First, we give some readily-checked conditions on measurement noises and sensor deployment to guarantee the asymptotic identifiability of the model and show the…

Signal Processing · Electrical Eng. & Systems 2023-09-26 Guangyang Zeng , Biqiang Mu , Ling Shi , Jiming Chen , Junfeng Wu