Related papers: A note on concentration inequality for vector-valu…

Kwapien and Woyczynski asked in their monograph (1992) whether their notion of superstrong domination is inherited when taking sums of independent symmetric random vectors (one vector dominates another if, essentially, tail probabilities of…

We propose a new and interpretable class of high-dimensional tail dependence models based on latent linear factor structures. Specifically, extremal dependence of an observable vector is assumed to be driven by a lower-dimensional latent…

Whether an extreme observation is an outlier or not, depends strongly on the corresponding tail behaviour of the underlying distribution. We develop an automatic, data-driven method to identify extreme tail behaviour that deviates from the…

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 propose the notion of sub-Weibull distributions, which are characterised by tails lighter than (or equally light as) the right tail of a Weibull distribution. This novel class generalises the sub-Gaussian and sub-Exponential families to…

We study concentration inequalities for structured weighted sums of random data, including (i) tensor inner products and (ii) sequential matrix sums. We are interested in tail bounds and concentration inequalities for those structured…

Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the…

This note describes non-asymptotic variance and tail bounds for order statistics of samples of independent identically distributed random variables. Those bounds are checked to be asymptotically tight when the sampling distribution belongs…

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 paper deduces exponential matrix concentration from a Poincar\'e inequality via a short, conceptual argument. Among other examples, this theory applies to matrix-valued functions of a uniformly log-concave random vector. The proof…

We study the critical behavior of the component sizes for the configuration model when the tail of the degree distribution of a randomly chosen vertex is a regularly-varying function with exponent $\tau-1$, where $\tau\in (3,4)$. The…

The Entropy method provides a powerful framework for proving scalar concentration inequalities by establishing functional inequalities like Poincare and log-Sobolev inequalities. These inequalities are especially useful for deriving…

We investigate the use of optimization to compute bounds for extremal performance measures. This approach takes a non-parametric viewpoint that aims to alleviate the issue of model misspecification possibly encountered by conventional…

Building on the inequalities for homogeneous tetrahedral polynomials in independent Gaussian variables due to R. Lata{\l}a we provide a concentration inequality for non-necessarily Lipschitz functions $f\colon \R^n \to \R$ with bounded…

This paper extends classical probabilistic results to the broader class of demimartingales and demisubmartingales. We establish variants of Doob's-type optional sampling theorem under minimal structural conditions on stopping times, relying…

We study one-dimensional functional inequalities of the type of Poincar\'e, logarithmic Sobolev and Wirtinger, with weight, for probability densities with polynomial tails. As main examples, we obtain sharp inequalities satisfied by inverse…

A common bottleneck in evaluating extremal performance measures is that, due to their very nature, tail data are often very limited. The conventional approach selects the best probability distribution from tail data using parametric…

Linear regression with the classical normality assumption for the error distribution may lead to an undesirable posterior inference of regression coefficients due to the potential outliers. This paper considers the finite mixture of two…

We study the joint laws of a continuous, uniformly integrable martingale, its maximum, and its minimum. In particular, we give explicit martingale inequalities which provide upper and lower bounds on the joint exit probabilities of a…

We consider directed polymers in random environment on the lattice Z d at small inverse temperature and dimension d $\ge$ 3. Then, the normalized partition function W n is a regular martingale with limit W. We prove that n (d--2)/4 (W n --…