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We derive generalization error bounds for the training of two-layer neural networks without assuming boundedness of the loss function, using Wasserstein distance estimates on the discrepancy between a probability distribution and its…

Machine Learning · Statistics 2026-04-09 Jiang Yu Nguwi , Nicolas Privault

We consider a distributed optimization problem over a network of agents aiming to minimize a global objective function that is the sum of local convex and composite cost functions. To this end, we propose a distributed Chebyshev-accelerated…

Optimization and Control · Mathematics 2018-10-17 Jacob H. Seidman , Mahyar Fazlyab , George J. Pappas , Victor M. Preciado

This paper studies the problem of computing a linear approximation of quadratic Wasserstein distance $W_2$. In particular, we compute an approximation of the negative homogeneous weighted Sobolev norm whose connection to Wasserstein…

Numerical Analysis · Mathematics 2022-03-02 Philip Greengard , Jeremy G. Hoskins , Nicholas F. Marshall , Amit Singer

In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…

Data Analysis, Statistics and Probability · Physics 2024-07-16 Taki Kirouani

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…

Optimization and Control · Mathematics 2025-05-30 Jun Fan , Ailing Yan , Xianchao Xiu , Wanquan Liu

Using quasi-Newton methods in stochastic optimization is not a trivial task given the difficulty of extracting curvature information from the noisy gradients. Moreover, pre-conditioning noisy gradient observations tend to amplify the noise.…

Optimization and Control · Mathematics 2024-04-02 Andre Carlon , Luis Espath , Raul Tempone

This work discusses how to derive upper bounds for the expected generalisation error of supervised learning algorithms by means of the chaining technique. By developing a general theoretical framework, we establish a duality between…

Machine Learning · Statistics 2022-07-01 Eugenio Clerico , Amitis Shidani , George Deligiannidis , Arnaud Doucet

We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…

Statistics Theory · Mathematics 2024-02-14 Aryeh Kontorovich , Amichai Painsky

Given a compact subset of a Banach space, the Chebyshev center problem consists of finding a minimal circumscribing ball containing the set. In this article we establish a numerically tractable algorithm for solving the Chebyshev center…

Optimization and Control · Mathematics 2023-07-06 Pradyumna Paruchuri , Debasish Chatterjee

This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…

Machine Learning · Computer Science 2016-09-13 Steve Hanneke

This paper is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal…

Statistics Theory · Mathematics 2024-12-10 Bernard Bercu , Jérémie Bigot

We establish novel rates for the Gaussian approximation of random deep neural networks with Gaussian parameters (weights and biases) and Lipschitz activation functions, in the wide limit. Our bounds apply for the joint output of a network…

Statistics Theory · Mathematics 2023-12-20 Dario Trevisan

Despite the strong predictive performance achieved by machine learning models across many application domains, assessing their trustworthiness through reliable estimates of predictive confidence remains a critical challenge. This issue…

Machine Learning · Computer Science 2026-03-25 Abolfazl Mohammadi-Seif , Carlos Soares , Rita P. Ribeiro , Ricardo Baeza-Yates

The training and test data for deep-neural-network-based classifiers are usually assumed to be sampled from the same distribution. When part of the test samples are drawn from a distribution that is sufficiently far away from that of the…

Machine Learning · Computer Science 2021-12-14 Yinan Wang , Wenbo Sun , Jionghua "Judy" Jin , Zhenyu "James" Kong , Xiaowei Yue

Correctly estimating the discrepancy between two data distributions has always been an important task in Machine Learning. Recently, Cuturi proposed the Sinkhorn distance which makes use of an approximate Optimal Transport cost between two…

Computer Vision and Pattern Recognition · Computer Science 2018-01-18 Ying Lu , Liming Chen , Alexandre Saidi , Xianfeng Gu

An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…

Optimization and Control · Mathematics 2026-04-02 Albert S. Berahas , Frank E. Curtis , Lara Zebiane

We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and…

Machine Learning · Computer Science 2020-03-18 Yi Hao , Alon Orlitsky

All 21-cm signal experiments rely on electronic receivers that affect the data via both multiplicative and additive biases through the receiver's gain and noise temperature. While experiments attempt to remove these biases, the residuals of…

Cosmology and Nongalactic Astrophysics · Physics 2021-07-14 Keith Tauscher , David Rapetti , Bang D. Nhan , Alec Handy , Neil Bassett , Joshua Hibbard , David Bordenave , Richard F. Bradley , Jack O. Burns

We investigate the problem of synthesizing distributionally robust control policies for stochastic systems under safety and reach-avoid specifications. Using a game-theoretical framework, we consider the setting where the probability…

Systems and Control · Electrical Eng. & Systems 2025-11-04 Yu Chen , Yuda Li , Shaoyuan Li , Xiang Yin

We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…

Statistics Theory · Mathematics 2020-11-13 Christos Tzamos , Emmanouil-Vasileios Vlatakis-Gkaragkounis , Ilias Zadik