Related papers: Concentration inequalities for sampling without re…
In this work we provide performance guarantees for hypocoercive non-reversible MCMC samplers $X_t$ with invariant measure $\mu_*$; our results apply in particular to the Langevin equation, Hamiltonian Monte-Carlo, and the bouncy particle…
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…
We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for classical Markov chains which provide constraints on finite time fluctuations of time-additive…
We show that the mixing times of random walks on compact groups can be used to obtain concentration inequalities for the respective Haar measures. As an application, we derive a concentration inequality for the empirical distribution of…
The phenomenon of entropy concentration provides strong support for the maximum entropy method, MaxEnt, for inferring a probability vector from information in the form of constraints. Here we extend this phenomenon, in a discrete setting,…
We derive tight and computable bounds on the bias of statistical estimators, or more generally of quantities of interest, when evaluated on a baseline model P rather than on the typically unknown true model Q. Our proposed method combines…
We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit…
Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and,…
Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.
Many inference problems, such as sequential decision problems like A/B testing, adaptive sampling schemes like bandit selection, are often online in nature. The fundamental problem for online inference is to provide a sequence of confidence…
Let $T$ be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry--Esseen type bounds for $T$ are obtained. The bounds are the best possible for many known statistics.…
For noncorrelated random variables, we study a concentration property of the family of distributions of normalized sums formed by sequences of times of a given large length.
Consider a discrete memoryless multiple source with $m$ components of which $k \leq m$ possibly different sources are sampled at each time instant and jointly compressed in order to reconstruct all the $m$ sources under a given distortion…
Barycenters (aka Fr\'echet means) were introduced in statistics in the 1940's and popularized in the fields of shape statistics and, later, in optimal transport and matrix analysis. They provide the most natural extension of linear…
In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…
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.…
When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…
We consider a sequence of identically independently distributed random samples from an absolutely continuous probability measure in one dimension with unbounded density. We establish a new rate of convergence of the $\infty-$Wasserstein…
We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration…
Most NLP datasets are not annotated with protected attributes such as gender, making it difficult to measure classification bias using standard measures of fairness (e.g., equal opportunity). However, manually annotating a large dataset…