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We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…

Machine Learning · Computer Science 2016-11-04 P Balamurugan , Francis Bach

Heavy-tailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closed-form in graphical models which involve such heavy-tailed distributions. In this work, we…

Machine Learning · Computer Science 2011-03-22 Danny Bickson , Carlos Guestrin

We reconsider a classical, well-studied problem from applied probability. This is the max-sum equivalence of randomly weighted sums, and the originality is because we manage to include interdependence among the primary random variables, as…

The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…

Statistics Theory · Mathematics 2026-05-06 Stephan Clémençon , Anne Sabourin

We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior…

Probability · Mathematics 2016-01-07 Archil Gulisashvili , Peter Tankov

In this article we introduce a new method for the construction of unique strong solutions of a larger class of stochastic delay equations driven by a discontinuous drift vector field and a Wiener process. The results obtained in this paper…

Probability · Mathematics 2017-09-22 D. Baños , H. H. Haferkorn , F. Proske

This work has been motivated by the challenge of the 2017 conference on Extreme-Value Analysis (EVA2017), with the goal of predicting daily precipitation quantiles at the $99.8\%$ level for each month at observed and unobserved locations.…

Methodology · Statistics 2018-02-06 Thomas Opitz , Raphaël Huser , Haakon Bakka , Håvard Rue

We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…

Optimization and Control · Mathematics 2021-06-15 Vladislav Tominin , Yaroslav Tominin , Ekaterina Borodich , Dmitry Kovalev , Alexander Gasnikov , Pavel Dvurechensky

We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…

Probability · Mathematics 2018-02-05 Ulrich K. Mueller

The asymptotic tail behaviour of sums of independent subexponential random variables is well understood, one of the main characteristics being the principle of the single big jump. We study the case of dependent subexponential random…

Probability · Mathematics 2017-11-29 Sergey Foss , Andrew Richards

This paper presents precise large deviation estimates for solutions to stochastic fixed point equations of the type V =_d f(V), where f(v) = Av + g(v) for a random function g(v) = o(v) a.s. as v tends to infinity. Specifically, we provide…

Probability · Mathematics 2011-03-15 Jeffrey F. Collamore , Anand N. Vidyashankar

In this paper we study the joint distributional convergence of the largest eigenvalues of the sample covariance matrix of a $p$-dimensional time series with iid entries when $p$ converges to infinity together with the sample size $n$. We…

Probability · Mathematics 2016-08-26 Johannes Heiny , Thomas Mikosch

In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large…

Statistics Theory · Mathematics 2015-09-02 T. Mikosch , O. Wintenberger

We propose an inertial variant of the strongly convergent inexact proximal-point (PP) method of Solodov and Svaiter (2000) for monotone inclusions. We prove strong convergence of our main algorithm under less restrictive assumptions on the…

Optimization and Control · Mathematics 2025-09-24 M. Marques Alves , J. E. Navarro Caballero , M. Geremia , R. T. Marcavillaca

Both parametric distribution functions appearing in extreme value theory - the generalized extreme value distribution and the generalized Pareto distribution - have log-concave densities if the extreme value index gamma is in [-1,0].…

Statistics Theory · Mathematics 2023-04-17 Samuel Müller , Kaspar Rufibach

Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…

Methodology · Statistics 2022-07-26 Yongxin Li , Liujun Chen , Deyuan Li , Hansheng Wang

Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…

Optimization and Control · Mathematics 2020-10-16 Ernst Roos , Ruud Brekelmans , Wouter van Eekelen , Dick den Hertog , Johan van Leeuwaarden

Recently a functional limit theorem for sums of moving averages with random coefficients and i.i.d. heavy tailed innovations has been obtained under the assumption that all partial sums of the series of coefficients are a.s. bounded between…

Probability · Mathematics 2021-09-27 Danijel Krizmanić

High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square…

Statistics Theory · Mathematics 2019-10-02 Jun Zhao , Guan'ao Yan , Yi Zhang

In this paper, we obtain some results on precise large deviations for non-random and random sums of widely dependent random variables with common dominatedly varying tail distribution or consistently varying tail distribution on…

Probability · Mathematics 2021-06-14 Zhaolei Cui , Yuebao Wang