Related papers: Lower tails via relative entropy
This paper examines the performance of ridge regression in reproducing kernel Hilbert spaces in the presence of noise that exhibits a finite number of higher moments. We establish excess risk bounds consisting of subgaussian and polynomial…
We derive in this preprint the moment and exponential tail estimates, sufficient conditions for the Non-Central Limit Theorem (NCLT) in the ordinary one-dimensional space as well as in the space of continuous functions for the properly…
Although there is an extensive literature on the maxima of Gaussian processes, there are relatively few non-asymptotic bounds on their lower-tail probabilities. The aim of this paper is to develop such a bound, while also allowing for many…
Amit and Linial showed that a random lift of a graph with minimum degree $\delta\ge3$ is asymptotically almost surely $\delta$-connected, and mentioned the problem of estimating this probability as a function of the degree of the lift. We…
A graph $G$ is said to be $p$-locally dense if every induced subgraph of $G$ with linearly many vertices has edge density at least $p$. A famous conjecture of Kohayakawa, Nagle, R\"odl, and Schacht predicts that locally dense graphs have,…
Recent studies have provided both empirical and theoretical evidence illustrating that heavy tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy tails potentially result in iterates with diverging…
Link prediction, as a fundamental task for graph neural networks (GNNs), has boasted significant progress in varied domains. Its success is typically influenced by the expressive power of node representation, but recent developments reveal…
Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This…
We prove tail estimates for variables $\sum_i f(X_i)$, where $(X_i)_i$ is the trajectory of a random walk on an undirected graph (or, equivalently, a reversible Markov chain). The estimates are in terms of the maximum of the function $f$,…
In this work, we study the convergence \emph{in high probability} of clipped gradient methods when the noise distribution has heavy tails, ie., with bounded $p$th moments, for some $1<p\le2$. Prior works in this setting follow the same…
This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…
What is the probability that the number of triangles in $\mathcal{G}_{n,p}$, the Erd\H{o}s-R\'enyi random graph with edge density $p$, is at least twice its mean? Writing it as $\exp[- r(n,p)]$, already the order of the rate function…
We study randomly coloured graphs embedded into Euclidean space, whose vertex sets are infinite, uniformly discrete subsets of finite local complexity. We construct the appropriate ergodic dynamical systems, explicitly characterise ergodic…
We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…
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…
The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are…
In high-dimensions, the prior tails can have a significant effect on both posterior computation and asymptotic concentration rates. To achieve optimal rates while keeping the posterior computations relatively simple, an empirical Bayes…
We consider the problem of finding the optimal upper bound for the tail probability of a sum of $k$ nonnegative, independent and identically distributed random variables with given mean $x$. For $k=1$ the answer is given by Markov's…
The degree distribution is one of the most fundamental graph properties of interest for real-world graphs. It has been widely observed in numerous domains that graphs typically have a tailed or scale-free degree distribution. While the…
The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…