相关论文: Singletons for Simpletons: Revisiting Windowed Bac…

We consider a multivariate distributional recursion of sum-type as arising in the probabilistic analysis of algorithms and random trees. We prove an upper tail bound for the solution using Chernoff's bounding technique by estimating the…

The study of {\em balls-into-bins processes} or {\em occupancy problems} has a long history. These processes can be used to translate realistic problems into mathematical ones in a natural way. In general, the goal of a balls-into-bins…

Consider throwing $n$ balls at random into $m$ urns, each ball landing in urn $i$ with probability $p_i$. Let $S$ be the resulting number of singletons, i.e., urns containing just one ball. We give an error bound for the Kolmogorov distance…

We study a higher-dimensional 'balls-into-bins' problem. An infinite sequence of i.i.d. random vectors is revealed to us one vector at a time, and we are required to partition these vectors into a fixed number of bins in such a way as to…

Consider a finite number of balls initially placed in $L$ bins. At each time step a ball is taken from each non-empty bin. Then all the balls are uniformly reassigned into bins. This finite Markov chain is called Repeated Balls-into-Bins…

An identity between two versions of the Chernoff bound on the probability a certain large deviations event, is established. This identity has an interpretation in statistical physics, namely, an isothermal equilibrium of a composite system…

Recent research has made significant progress on the problem of bounding log partition functions for exponential family graphical models. Such bounds have associated dual parameters that are often used as heuristic estimates of the marginal…

Using coupling techniques based on Stein's method for probability approximation, we revisit classical variance bounding inequalities of Chernoff, Cacoullos, Chen and Klaassen. Taking advantage of modern coupling techniques allows us to…

We revisit the random allocation model in which $n$ balls are independently placed into $N$ boxes with probabilities $q_1,\ldots,q_N$. A classical asymptotic result due to Kolchin, Sevastyanov, and Chistyakov for the expectations,…

We consider the unbalanced allocation of $m$ balls into $n$ bins by a randomized algorithm using the "power of two choices". For each ball, we select a set of bins at random, then place the ball in the fullest bin within the set.…

Almost 10 years ago, Impagliazzo and Kabanets (2010) gave a new combinatorial proof of Chernoff's bound for sums of bounded independent random variables. Unlike previous methods, their proof is constructive. This means that it provides an…

We take a unified approach to central limit theorems for a class of irreducible urn models with constant replacement matrix. Depending on the eigenvalue, we consider appropriate linear combinations of the number of balls of different…

Azuma's inequality is a tool for proving concentration bounds on random variables. The inequality can be thought of as a natural generalization of additive Chernoff bounds. On the other hand, the analogous generalization of multiplicative…

This work studies the problem of separate random number generation from correlated general sources with side information at the tester under the criterion of statistical distance. Tight one-shot lower and upper performance bounds are…

This paper describes the construction of a lower bound for the tails of general random variables, using solely knowledge of their moment generating function. The tilting procedure used allows for the construction of lower bounds that are…

It is common to encounter large-scale monotone inclusion problems where the objective has a finite sum structure. We develop a general framework for variance-reduced forward-backward splitting algorithms for this problem. This framework…

Chernoff bound is a fundamental tool in theoretical computer science. It has been extensively used in randomized algorithm design and stochastic type analysis. Discrepancy theory, which deals with finding a bi-coloring of a set system such…

This paper explores the distribution of indistinguishable balls into distinct urns with varying capacity constraints, a foundational issue in combinatorial mathematics with applications across various disciplines. We present a comprehensive…

In this paper, we develop a general approach for probabilistic estimation and optimization. An explicit formula and a computational approach are established for controlling the reliability of probabilistic estimation based on a mixed…

When it is ethical and legal to use a sensitive attribute (such as gender or race) in machine learning systems, the question remains how to do so. We show that the naive application of machine learning algorithms using sensitive features…