Related papers: The Distributional Tail of Worst-Case Quickselect

Models for extreme values are generally derived from limit results, which are meant to be good enough approximations when applied to finite samples. Depending on the speed of convergence of the process underlying the data, these…

Using tail bounds, we introduce a new probabilistic condition for function estimation in stochastic derivative-free optimization which leads to a reduction in the number of samples and eases algorithmic analyses. Moreover, we develop simple…

In this paper, we provide novel optimal (or near optimal) convergence rates for a clipped version of the stochastic subgradient method. We consider nonsmooth convex problems over possibly unbounded domains, under heavy-tailed noise that…

We study the problem of heavy-tailed mean estimation in settings where the variance of the data-generating distribution does not exist. Concretely, given a sample $\mathbf{X} = \{X_i\}_{i = 1}^n$ from a distribution $\mathcal{D}$ over…

The multidimensional distributions with heavy tails attracted recently the attention of several papers on Applied Probability. However, the most of the works of the last decades are focused on multivariate regular variation, while the rest…

We study the generalization properties of unregularized gradient methods applied to separable linear classification -- a setting that has received considerable attention since the pioneering work of Soudry et al. (2018). We establish tight…

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…

Constant-specified and exponential concentration inequalities play an essential role in the finite-sample theory of machine learning and high-dimensional statistics area. We obtain sharper and constants-specified concentration inequalities…

This work explores the bounds of the variance of unilaterally truncated Gaussian distributions (UTGDs) and scaled chi distributions (UTSCDs) with fixed means. For any arbitrary Gaussian distribution function, $f(x;\mu,\sigma)$, with a…

A sharp, distribution free, non-asymptotic result is proved for the concentration of a random function around the mean function, when the randomization is generated by a finite sequence of independent data and the random functions satisfy…

A simple way of obtaining robust estimates of the "center" (or the "location") and of the "scatter" of a dataset is to use the maximum likelihood estimate with a class of heavy-tailed distributions, regardless of the "true" distribution…

In the "stochastic $\delta N$ formalism", the statistics of the inflationary density perturbation are obtained from the first passage distribution of a stochastic process. We develop a general framework in which to evaluate the rare tail of…

We consider a class of hypothesis testing problems where the null hypothesis postulates $M$ distributions for the observed data, and there is only one possible distribution under the alternative. We show that one can use a stochastic mirror…

We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…

We consider the \mnk{classical} problem of a controller activating (or sampling) sequentially from a finite number of $N \geq 2$ populations, specified by unknown distributions. Over some time horizon, at each time $n = 1, 2, \ldots$, the…

While numerous works have focused on devising efficient algorithms for reinforcement learning (RL) with uniformly bounded rewards, it remains an open question whether sample or time-efficient algorithms for RL with large state-action space…

We study the replacement paths problem in the $\mathsf{CONGEST}$ model of distributed computing. Given an $s$-$t$ shortest path $P$, the goal is to compute, for every edge $e$ in $P$, the shortest-path distance from $s$ to $t$ avoiding $e$.…

We study a new estimator for the tail index of a distribution in the Frechet domain of attraction that arises naturally by computing subsample maxima. This estimator is equivalent to taking a U-statistic over a Hill estimator with two order…

We study the dynamics of a continuous-time model of the Stochastic Gradient Descent (SGD) for the least-square problem. Indeed, pursuing the work of Li et al. (2019), we analyze Stochastic Differential Equations (SDEs) that model SGD either…

We establish maximal concentration bounds for the iterates generated by stochastic approximation algorithms with general step sizes, where the noise has a finite-state Markovian component plus a Martingale-difference component. When the…