Related papers: Tail bounds via generic chaining

We study moderate deviations of suprema of parametrized sequences of sample bounded Gaussian processes $\{X _x(t), t\in T _x\}$, and first present recent sharp bounds in simple cases. In the almost periodic case, we prove an approximation…

Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…

We study convergence lower bounds of without-replacement stochastic gradient descent (SGD) for solving smooth (strongly-)convex finite-sum minimization problems. Unlike most existing results focusing on final iterate lower bounds in terms…

This paper develops a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating whole empirical processes in the sup-norm. We prove…

We give a concise self-contained presentation of known and new limit theorems for the one-type Markov branching processes with continuous time. The new streamlined proofs are based on what we call, the tail generating function approach. Our…

This paper integrates manifold learning techniques within a \emph{Gaussian process upper confidence bound} algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of…

In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…

We prove that the tail probabilities of sums of independent uniform random variables, up to a multiplicative constant, are dominated by the Gaussian tail with matching variance and find the sharp constant for such stochastic domination.

This is Part II of our work about random tensor inequalities and tail bounds for bivariate random tensor means. After reviewing basic facts about random tensors, we first consider tail bounds with more general connection functions. Then, a…

We study the finite-time behaviour of the popular temporal difference (TD) learning algorithm when combined with tail-averaging. We derive finite time bounds on the parameter error of the tail-averaged TD iterate under a step-size choice…

Gradient clipping is a commonly used technique to stabilize the training process of neural networks. A growing body of studies has shown that gradient clipping is a promising technique for dealing with the heavy-tailed behavior that emerged…

In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…

We consider the task of heavy-tailed statistical estimation given streaming $p$-dimensional samples. This could also be viewed as stochastic optimization under heavy-tailed distributions, with an additional $O(p)$ space complexity…

We establish Hoeffding-type concentration inequalities for the low and high tail bounds of sums of exchangeable random variables. Our results exhibit an anti-symmetry in such tail bounds due to the assumption of exchangeability, a…

We consider non-convex stochastic optimization using first-order algorithms for which the gradient estimates may have heavy tails. We show that a combination of gradient clipping, momentum, and normalized gradient descent yields convergence…

This paper develops a general concentration inequality for the suprema of empirical processes with dependent data. The concentration inequality is obtained by combining generic chaining with a coupling-based strategy. Our framework…

In the paper we consider higher-order partial differential equations from the class of linear dispersive equations. We investigate solutions to these equations subject to random initial conditions given by harmonizable…

In this paper, we provide novel tail bounds on the optimization error of Stochastic Mirror Descent for convex and Lipschitz objectives. Our analysis extends the existing tail bounds from the classical light-tailed Sub-Gaussian noise case to…

We derive uniform concentration inequalities for continuous-time analogues of empirical processes and related stochastic integrals of scalar ergodic diffusion processes. Thereby, we lay the foundation typically required for the study of…

An asymptotic model for extreme behavior of certain Markov chains is the "tail chain". Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics such as point process limits. We place this…