Related papers: A concentration inequality for product spaces
We show that the product of any number of sequentially pseudocompact topological spaces is still sequentially pseudocompact. The definition of sequential pseudocompactness can be given in (at least) two ways: we show their equivalence. Some…
We prove a new and general concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise. No specific structure is required on the model, except the existence of a suitable function…
Several Artificial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncertain domain models. Even though the correct working of these…
In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm bounded random vectors), which are tight up to logarithmic factors.
Let q^n be a continuous density function in n-dimensional Euclidean space. We think of q^n as the density function of some random sequence X^n with values in \BbbR^n. For I\subset[1,n], let X_I denote the collection of coordinates X_i, i\in…
We present a class of inequality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network, in which some of the variables remain unmeasured. We derive bounds on causal effects…
We show that any probability measure satisfying a Matrix Poincar\'e inequality with respect to some reversible Markov generator satisfies an exponential matrix concentration inequality depending on the associated matrix carr\'e du champ…
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…
We present a measure-theoretic condition for a property to hold ``almost everywhere'' on an infinite-dimensional vector space, with particular emphasis on function spaces such as $C^k$ and $L^p$. Like the concept of ``Lebesgue almost…
We give a simple development of the concentration properties of compound Poisson measures on the nonnegative integers. A new modification of the Herbst argument is applied to an appropriate modified logarithmic-Sobolev inequality to derive…
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are independent and identically distributed…
In this paper we prove the S-inequality for certain product probability measures and ideals in R^n . As a result, for the Weibull and Gamma product distributions we derive concentration of measure type estimates as well as optimal…
Nonprobability (convenience) samples are increasingly sought to stabilize estimations for one or more population variables of interest that are performed using a randomized survey (reference) sample by increasing the effective sample size.…
We present a concentration inequality for linear functionals of noncommutative polynomials in random matrices. Our hypotheses cover most standard ensembles, including Gaussian matrices, matrices with independent uniformly bounded entries…
We formulate simple equivalent conditions for the validity of Bayes' formula for conditional densities. We show that for any random variables X and Y (with values in arbitrary measurable spaces), the following are equivalent: 1. X and Y…
We prove logarithmic Sobolev inequalities and concentration results for convex functions and a class of product random vectors. The results are used to derive tail and moment inequalities for chaos variables (in spirit of Talagrand and…
Algorithmic recommendation based on noisy preference measurement is prevalent in recommendation systems. This paper discusses the consequences of such recommendation on market concentration and inequality. Binary types denoting a…
We prove concentration inequalities for general functions of weakly dependent random variables satisfying the Dobrushin condition. In particular, we show Talagrand's convex distance inequality for this type of dependence. We apply our…
In the context of interacting particle systems, we study the influence of the action of the semigroup on the concentration property of Lipschitz functions. As an application, this gives a new approach to estimate the relaxation speed to…
The aim of this paper is to prove an inequality between relative entropy and the sum of average conditional relative entropies of the following form: For a fixed probability measure $q^n$ on $\mathcal X^n$, ($\mathcal X$ is a finite set),…