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Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep…

Machine Learning · Statistics 2019-06-24 Thanh Huy Nguyen , Umut Şimşekli , Mert Gürbüzbalaban , Gaël Richard

We propose a novel approach for quantifying deviations from Gaussianity by leveraging the permutation Jensen-Shannon distance. Using stable distributions as a flexible framework, we analyze the effects of skewness and heavy tails in…

Physics and Society · Physics 2025-03-31 Felipe Olivares , Massimiliano Zanin

In this note, we apply Stein's method to analyze the steady-state distribution of queueing systems in the traditional heavy-traffic regime. Compared to previous methods (e.g., drift method and transform method), Stein's method allows us to…

Probability · Mathematics 2020-10-08 Xingyu Zhou , Ness Shroff

We investigate the tail asymptotic behavior of the sojourn time for a large class of centered Gaussian processes $X$, in both continuous- and discrete-time framework. All results obtained here are new for the discrete-time case. In the…

Probability · Mathematics 2017-12-14 Krzysztof Dȩbicki , Enkelejd Hashorva , Xiaofan Peng , Zbigniew Michna

We develop accurate approximations of the delay distribution of the MArP/G/1 queue that cap- ture the exact tail behavior and provide bounded relative errors. Motivated by statistical analysis, we consider the service times as a mixture of…

Probability · Mathematics 2014-05-21 Eleni Vatamidou , Ivo J. B. F. Adan , Maria Vlasiou , Bert Zwart

The default Gaussian latent in flow-based generative models poses challenges when learning certain distributions such as heavy-tailed ones. We introduce a general framework for learning data-adaptive latent distributions using…

Machine Learning · Statistics 2026-02-11 Jannis Chemseddine , Gregor Kornhardt , Richard Duong , Gabriele Steidl

Neural network compression techniques have become increasingly popular as they can drastically reduce the storage and computation requirements for very large networks. Recent empirical studies have illustrated that even simple pruning…

Machine Learning · Statistics 2021-06-08 Melih Barsbey , Milad Sefidgaran , Murat A. Erdogdu , Gaël Richard , Umut Şimşekli

Consider a first-come, first-served single server queue with an initial workload $x>0$ and customers who arrive according to an inhomogeneous Poisson process with rate function $\lambda:[0,\infty)\rightarrow[0,\lambda_h ]$ for some…

Probability · Mathematics 2025-03-18 Shreehari Anand Bodas , Royi Jacobovic

We consider a queueing network operating under a strictly upper-triangular routing matrix with per column at most one non-negative entry. The root node is fed by a Gaussian process with stationary increments. Our aim is to characterize the…

Probability · Mathematics 2025-03-24 Nikolai Kriukov , Krzysztof Dȩbicki , Michel Mandjes

This paper investigates tail asymptotics of stationary distributions and quasi-stationary distributions (QSDs) of continuous-time Markov chains on subsets of the non-negative integers. Based on the so-called flux-balance equation, we…

Probability · Mathematics 2023-08-16 Chuang Xu , Mads Christian Hansen , Carsten Wiuf

Economically responsible mitigation of multivariate extreme risks-such as extreme rainfall over large areas, large simultaneous variations in many stock prices, or widespread breakdowns in transportation systems-requires assessing the…

Machine Learning · Statistics 2026-01-13 Stéphane Lhaut , Holger Rootzén , Johan Segers

We study the behavior of the posterior distribution in high-dimensional Bayesian Gaussian linear regression models having $p\gg n$, with $p$ the number of predictors and $n$ the sample size. Our focus is on obtaining quantitative finite…

Statistics Theory · Mathematics 2014-01-06 Nate Strawn , Artin Armagan , Rayan Saab , Lawrence Carin , David Dunson

We study the self-normalized concentration of vector-valued stochastic processes. We focus on bounds for "sub-$\psi$" processes, a well-known and quite general class of process that encompasses a wide variety of well-known tail conditions…

Probability · Mathematics 2026-02-06 Ben Chugg , Aaditya Ramdas

Given a single observation from a Gaussian distribution with unknown mean $\theta$, we design computationally efficient procedures that can approximately generate an observation from a different target distribution $Q_{\theta}$ uniformly…

Statistics Theory · Mathematics 2025-10-09 Mengqi Lou , Guy Bresler , Ashwin Pananjady

Bounding the queue length in a multiserver queue is a central challenge in queueing theory. Even for the classical $G/G/n$ queue with homogeneous servers, it is highly non-trivial to derive a simple and accurate bound for the steady-state…

Probability · Mathematics 2026-04-07 Yige Hong

The infinite source Poisson arrival model with heavy-tailed workload distributions has attracted much attention, especially in the modeling of data packet traffic in communication networks. In particular, it is well known that under…

Probability · Mathematics 2012-10-30 Amarjit Budhiraja , Vladas Pipiras , Xiaoming Song

We consider a heterogeneous queueing system consisting of one large pool of $O(r)$ identical servers, where $r\to\infty$ is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in…

Probability · Mathematics 2011-05-04 David Gamarnik , Alexander Stolyar

We consider the model of a token-based joint auto-scaling and load balancing strategy, proposed in a recent paper by Mukherjee, Dhara, Borst, and van Leeuwaarden (SIGMETRICS '17, arXiv:1703.08373), which offers an efficient scalable…

Probability · Mathematics 2020-02-27 Debankur Mukherjee , Alexander Stolyar

In this paper we consider the problem of obtaining sharp bounds for the performance of temporal difference (TD) methods with linear function approximation for policy evaluation in discounted Markov decision processes. We show that a simple…

Machine Learning · Statistics 2024-06-18 Sergey Samsonov , Daniil Tiapkin , Alexey Naumov , Eric Moulines

Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is…

Methodology · Statistics 2024-05-01 Arnab Hazra , Raphaël Huser , David Bolin