Related papers: Concentration inequality using unconfirmed knowled…
In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means $\{ \mu_1, \mu_2, \mu_3\}$ through an analysis of variance…
The conditional entropy power inequality is a fundamental inequality in information theory, stating that the conditional entropy of the sum of two conditionally independent vector-valued random variables each with an assigned conditional…
The classical Gaussian concentration inequality for Lipschitz functions is adapted to a setting where the classical assumptions (i.e. Lipschitz and Gaussian) are not met. The theory is more direct than much of the existing theory designed…
We derive novel anti-concentration bounds for the difference between the maximal values of two Gaussian random vectors across various settings. Our bounds are dimension-free, scaling with the dimension of the Gaussian vectors only through…
Concentration of measure is a phenomenon in which a random variable that depends in a smooth way on a large number of independent random variables is essentially constant. The random variable will "concentrate" around its median or…
In this expository note, we give a modern proof of Hanson-Wright inequality for quadratic forms in sub-gaussian random variables. We deduce a useful concentration inequality for sub-gaussian random vectors. Two examples are given to…
This paper studies Hoeffding's inequality for Markov chains under the generalized concentrability condition defined via integral probability metric (IPM). The generalized concentrability condition establishes a framework that interpolates…
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…
We give a simple inequality for the sum of independent bounded random variables. This inequality improves on the celebrated result of Hoeffding in a special case. It is optimal in the limit where the sum tends to a Poisson random variable.
Considering a general framework of bootstrap with exchangeable weights, we show some concentration inequalities for the supremum of the bootstrap empirical process. On the one hand, we discuss the concentration of the bootstrap empirical…
An infinite urn scheme is defined by a probability mass function $(p_j)_{j\geq1}$ over positive integers. A random allocation consists of a sample of $N$ independent drawings according to this probability distribution where $N$ may be…
The purpose of this dissertation is to introduce a version of Stein's method of exchangeable pairs to solve problems in measure concentration. We specifically target systems of dependent random variables, since that is where the power of…
Let $\boldsymbol{X}$ be a $d$-dimensional random array on $[n]$ whose entries take values in a finite set $\mathcal{X}$, that is, $\boldsymbol{X}=\langle X_s:s\in \binom{[n]}{d}\rangle$ is an $\mathcal{X}$-valued stochastic process indexed…
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.
This paper provides a systematic yet accessible presentation of the Contextuality-by-Default theory. The consideration is confined to finite systems of categorical random variables, which allows us to focus on the basics of the theory…
We study the estimation and concentration on its expectation of the probability to observe data further than a specified distance from a given iid sample in a metric space. The problem extends the classical problem of estimation of the…
The so-called pinball loss for estimating conditional quantiles is a well-known tool in both statistics and machine learning. So far, however, only little work has been done to quantify the efficiency of this tool for nonparametric…
Uncertainty principles for concentration of signals into truncated subspaces are considered. The ``classic'' uncertainty principle is explored as a special case of a more general operator framework. The time-bandwidth concentration problem…
By probabilistic means, the concept of contextuality is extended so that it can be used in non-ideal situations. An inequality is presented, which at least in principle enables a test to discard non-contextual hidden-variable models at low…
We consider the conditional randomization test as a way to account for covariate imbalance in randomized experiments. The test accounts for covariate imbalance by comparing the observed test statistic to the null distribution of the test…