相关论文: An extension of McDiarmid's inequality
Concentration inequalities are indispensable tools for studying the generalization capacity of learning models. Hoeffding's and McDiarmid's inequalities are commonly used, giving bounds independent of the data distribution. Although this…
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 present some extensions of Bernstein's concentration inequality for random matrices. This inequality has become a useful and powerful tool for many problems in statistics, signal processing and theoretical computer science. The main…
We prove an extension of McDiarmid's inequality for metric spaces with unbounded diameter. To this end, we introduce the notion of the {\em subgaussian diameter}, which is a distribution-dependent refinement of the metric diameter. Our…
We improve the rate function of McDiarmid's inequality for Hamming distance. In particular, applying our result to the separately Lipschitz functions of independent random variables, we also refine the convergence rate function of…
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…
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…
We give a concentration inequality based on the premise that random variables take values within a particular region. The concentration inequality guarantees that, for any sequence of correlated random variables, the difference between the…
This work extends the Mond-Pecaric method to functions with multiple operators as arguments by providing arbitrarily close approximations of the original functions. Instead of using linear functions to establish lower and upper bounds for…
Young's inequality is extended to the context of absolutely continuous measures. Several applications are included.
This paper aims to characterize the function appearing in the weighted Hermite-Hadamard inequality. We provide improved inequalities for the weighted means as applications of the obtained results. Modifications of the weighted…
In the setting of a metric space equipped with a doubling measure and supporting a Poincar\'e inequality, and based on results by Bj\"orn and Shanmugalingam (2007), we show that functions of bounded variation can be extended from any…
We give a statement on extension with estimates of convex functions defined on a linear subspace, inspired by similar extension results concerning metrics on positive line bundles
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
We show sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order $d-1$ for any $d \in \mathbb{N}$. Here we focus on differentiable functions on the Euclidean space in presence of a…
We extend the fundamental normality test due to Carath\'eodory in the sense of shared functions.
A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply…
In the paper, the authors introduce a new concept "extended $s$-convex functions", establish some new integral inequalities of Hermite-Hadamard type for this kind of functions, and apply these inequalities to derive some inequalities of…
Recently, extensions of gamma and beta functions have been studied by many researchers due to their nice properties and variety of applications in different fields of science. The aim of this note is to investigate generalized inequalities…
This paper is devoted to proving the general {\L}ojasiewicz inequality, in both the definable and subanalytic cases, under the most relaxed assumptions. It means that we drop the usual continuity and compactness assumptions. In the second…