Related papers: Concentration inequalities using higher moments in…
We investigate a convexity properties for normalized log moment generating function continuing a recent investigation of Chen of convex images of Gaussians. We show that any variable satisfying a ``Ehrhard-like'' property for its…
We establish concentration inequalities for Lipschitz functions of dependent random variables, whose dependencies are specified by forests. We also give concentration results for decomposable functions, improving Janson's Hoeffding-type…
Choosing models from a hypothesis space is a frequent task in approximation theory and inverse problems. Cross-validation is a classical tool in the learner's repertoire to compare the goodness of fit for different reconstruction models.…
While effective concentration inequalities for suprema of empirical processes exist under boundedness or strict tail assumptions, no comparable results have been available under considerably weaker assumptions. In this paper, we derive…
In this paper we prove multilevel concentration inequalities for bounded functionals $f = f(X_1, \ldots, X_n)$ of random variables $X_1, \ldots, X_n$ that are either independent or satisfy certain logarithmic Sobolev inequalities. The…
In this paper, we study moment and concentration inequalities for the spectral norm of sums of dependent random matrices. We establish novel Rosenthal-Burkholder inequalities for discrete-time matrix local martingales,…
We establish a universal framework for concentration inequalities based on invariance under diffeomorphism groups. Given a probability measure $\mu$ on a space $E$ and a diffeomorphism $\psi: E \to F$, concentration properties transfer…
Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…
We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained…
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…
We prove that in the context of general Markov semigroups Beckner inequalities with constants separated from zero as $p\to 1^+$ are equivalent to the modified log Sobolev inequality (previously only one implication was known to hold in this…
A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established…
This paper introduces a new $p$-dependent coercivity condition through which $L^p$-moments for solutions can be obtained for a large class of SPDEs in the variational framework. If $p=2$, our condition reduces to the classically coercivity…
We derive novel concentration inequalities that bound the statistical error for a large class of stochastic optimization problems, focusing on the case of unbounded objective functions. Our derivations utilize the following key tools: 1) A…
First-passage properties are central to the kinetics of target-search processes. Theoretical approaches so far primarily focused on predicting first-passage statistics for a given process or model. In practice, however, one faces the…
The data processing inequality is central to information theory and motivates the study of monotonic divergences. However, it is not clear operationally we need to consider all such divergences. We establish a simple method for Pinsker…
We prove concentration bounds for random Euclidean combinatorial optimization problems with $p$--costs. For bipartite matching and for the (mono- and bi-partite) traveling salesperson problem in dimension $d\ge 3$, we obtain concentration…
Concentration results say that a sequence of random variables becomes progressively concentrated around the mean. Such results are common in the study of functions of random graphs. We introduce a real-valued logic with various aggregate…
In recent work of Baik, Deift and Rains convergence of moments was established for the limiting joint distribution of the lengths of the first k rows in random Young tableaux. The main difficulty was obtaining a good estimate for the tail…
We obtain Rosenthal-type inequalities with sharp constants for moments of sums of independent random variables which are mixtures of a fixed distribution. We also identify extremisers in log-concave settings when the moments of summands are…