Related papers: Exponential Concentration Inequalities For Indepen…

In this paper we introduce and study the class of multivariate strong and strongly subexponential distributions. Some first properties are verified, as for example a type of multivariate analogue of Kesten's inequality, the closure property…

The concentration of measure phenomenon may be summarized as follows: a function of many weakly dependent random variables that is not too sensitive to any of its individual arguments will tend to take values very close to its expectation.…

In this paper, we provide a proof for the Hanson-Wright inequalities for sparsified quadratic forms in subgaussian random variables. This provides useful concentration inequalities for sparse subgaussian random vectors in two ways. Let $X =…

This paper presents a unified approach based on Wasserstein distance to derive concentration bounds for empirical estimates for two broad classes of risk measures defined in the paper. The classes of risk measures introduced include as…

We survey a few concentration inequalities for submodular and fractionally subadditive functions of independent random variables, implied by the entropy method for self-bounding functions. The power of these concentration bounds is that…

We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…

Consider any random graph model where potential edges appear independently, with possibly different probabilities, and assume that the minimum expected degree is omega(ln n). We prove that the adjacency matrix and the Laplacian of that…

Rank 1 inhomogeneous random graphs are a natural generalization of Erd\H{o}s R\'enyi random graphs. In this generalization each node is given a weight. Then the probability that an edge is present depends on the product of the weights of…

We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…

Hanson-Wright inequality provides a powerful tool for bounding the norm $|\xi|$ of a centered stochastic vector $\xi$ with sub-gaussian behavior. This paper extends the bounds to the case when $\xi$ only has bounded exponential moments of…

The paper focuses on general properties of parametric minimum contrast estimators. The quality of estimation is measured in terms of the rate function related to the contrast, thus allowing to derive exponential risk bounds invariant with…

We apply a variation on the methods of Duminil-Copin, Raoufi, and Tassion to establish a new differential inequality applying to both Bernoulli percolation and the Fortuin-Kasteleyn random cluster model. This differential inequality has a…

We present examples of $p$-sub-exponential random variables for any positive $p$. We prove two types of concentration of standard $p$-norms ($2$-norm is the Euclidean norm) of random vectors with independent $p$-sub-exponential coordinates…

We use a new method via $p$-Wasserstein bounds to prove Cram\'er-type moderate deviations in (multivariate) normal approximations. In the classical setting that $W$ is a standardized sum of $n$ independent and identically distributed…

Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…

Let $G$ be a random graph on the vertex set $\{1,2,..., n\}$ such that edges in $G$ are determined by independent random indicator variables, while the probability $p_{ij}$ for $\{i,j\}$ being an edge in $G$ is not assumed to be equal.…

We obtain non-uniform Edgeworth expansions for several classes of weakly dependent (non-stationary) sequences of random variables, including uniformly elliptic inhomogeneous Markov chains, random and time-varying (partially) hyperbolic or…

This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample…

We propose a novel approach to concentration for non-independent random variables. The main idea is to ``pretend'' that the random variables are independent and pay a multiplicative price measuring how far they are from actually being…

For any $\alpha\in (0,1)$ and any $n^{\alpha}\leq d\leq n/2$, we show that $\lambda(G)\leq C_\alpha \sqrt{d}$ with probability at least $1-\frac{1}{n}$, where $G$ is the uniform random $d$-regular graph on $n$ vertices, $\lambda(G)$ denotes…