Related papers: Sharp finite-sample concentration of independent v…

In this work, we investigate how to develop sharp concentration inequalities for sub-Weibull random variables, including sub-Gaussian and sub-exponential distributions. Although the random variables may not be sub-Guassian, the tail…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

We give a new proof of VC bounds where we avoid the use of symmetrization and use a shadow sample of arbitrary size. We also improve on the variance term. This results in better constants, as shown on numerical examples. Moreover our bounds…

Let $\{X_i\}_{i\geq1}$ be an i.i.d. sequence of random variables and define, for $n\geq2$, \[T_n=\cases{n^{-1/2}\hat{\sigma}_n^{-1}S_n,\quad \hat{\sigma}_n>0,\cr 0,\quad \hat{\sigma}_n=0,}with S_n=\sum_{i=1}^nX_i,…

Two new information-theoretic methods are introduced for establishing Poisson approximation inequalities. First, using only elementary information-theoretic techniques it is shown that, when $S_n=\sum_{i=1}^nX_i$ is the sum of the (possibly…

The fundamental result of Li, Long, and Srinivasan on approximations of set systems has become a key tool across several communities such as learning theory, algorithms, computational geometry, combinatorics and data analysis. The goal of…

This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…

Many management decisions involve accumulated random realizations for which only the first and second moments of their distribution are available. The sharp Chebyshev-type bound for the tail probability and Scarf bound for the expected loss…

This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit…

We prove the large deviation principle (LDP) for posterior distributions arising from subfamilies of full exponential families, allowing misspecification of the model. Moreover, motivated by the so-called inverse Sanov Theorem (see e.g.…

Asymptotics deviation probabilities of the sum S n = X 1 + $\times$ $\times$ $\times$ + X n of independent and identically distributed real-valued random variables have been extensively investigated , in particular when X 1 is not…

Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…

We provide a general framework to improve trade-offs between the number of full batch and sample queries used to solve structured optimization problems. Our results apply to a broad class of randomized optimization algorithms that…

The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…

In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…

We establish concentration inequalities for random dynamical systems (RDSs), assuming that the observables of interest are separately Lipschitz. Under a weak average contraction condition, we obtain deviation bounds for several random…

Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…

The approach of Kleitman (1970) and Kanter (1976) to multivariate concentration function inequalities is generalized in order to obtain for deviation probabilities of sums of independent symmetric random variables a lower bound depending…

Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…

Asymptotics deviation probabilities of the sum S n = X 1 + $\times$ $\times$ $\times$ + X n of independent and identically distributed real-valued random variables have been extensively investigated, in particular when X 1 is not…