Related papers: Concentration Inequalities for Exchangeable Tensor…
We prove that few largest (and most important) eigenvalues of random symmetric matrices of various kinds are very strongly concentrated. This strong concentration enables us to compute the means of these eigenvalues with high precision. Our…
We introduce a framework for systemic risk modeling in insurance portfolios using jointly exchangeable arrays, extending classical collective risk models to account for interactions. Joint exchangeability is a more general probabilistic…
In this paper, we generalize and improve some fundamental concentration inequalities using information on the random variables' higher moments. In particular, we improve the classical Hoeffding's and Bennett's inequalities for the case…
Random partition models are widely used in Bayesian methods for various clustering tasks, such as mixture models, topic models, and community detection problems. While the number of clusters induced by random partition models has been…
We prove a Bennett-type concentration bound for suprema of empirical processes based on sampling without replacement and a corresponding bound in the case of an arbitrary Hoeffding statistics. We improve on the previous results of such…
We derive a new closed-form variance-adaptive confidence sequence (CS) for estimating the average conditional mean of a sequence of bounded random variables. Empirically, it yields the tightest closed-form CS we have found for tracking…
We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy…
Most popular word embedding techniques involve implicit or explicit factorization of a word co-occurrence based matrix into low rank factors. In this paper, we aim to generalize this trend by using numerical methods to factor higher-order…
We derive tight bounds on the expected weights of several combinatorial optimization problems for random point sets of size $n$ distributed among the leaves of a balanced hierarchically separated tree. We consider {\it monochromatic} and…
Mixtures of $r$ independent distributions for two discrete random variables can be represented by matrices of nonnegative rank $r$. Likelihood inference for the model of such joint distributions leads to problems in real algebraic geometry…
This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
We present Hoeffding-type and Bernstein-type inequalities for right-censored data. The inequalities bound the difference between an inverse of the probability of censoring weighting (IPCW) estimator and its expectation. We first discuss the…
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…
Structured data summarization involves generation of natural language summaries from structured input data. In this work, we consider summarizing structured data occurring in the form of tables as they are prevalent across a wide variety of…
A central tool in the study of nonhomogeneous random matrices, the noncommutative Khintchine inequality, yields a nonasymptotic bound on the spectral norm of general Gaussian random matrices $X=\sum_i g_i A_i$ where $g_i$ are independent…
We consider ensembles of real symmetric band matrices with entries drawn from an infinite sequence of exchangeable random variables, as far as the symmetry of the matrices permits. In general the entries of the upper triangular parts of…
Shearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy. We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of…
We develop a class of exponential bounds for the probability that a martingale sequence crosses a time-dependent linear threshold. Our key insight is that it is both natural and fruitful to formulate exponential concentration inequalities…
The article presents new entropic continuity bounds for conditional expectations and conditional covariance matrices. These bounds are expressed in terms of the relative entropy between different coupling distributions. Our approach…