Related papers: Two new Probability inequalities and Concentration…
This paper presents compact notations for concentration inequalities and convenient results to streamline probabilistic analysis. The new expressions describe the typical sizes and tails of random variables, allowing for simple operations…
We consider two notions describing how one finite graph may be larger than another. Using them, we prove several theorems for such pairs that compare the number of spanning trees, the return probabilities of random walks, and the number of…
Random matrix theory has played an important role in recent work on statistical network analysis. In this paper, we review recent results on regimes of concentration of random graphs around their expectation, showing that dense graphs…
We introduce a version of Stein's method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical statistics are provided.
This survey provides an exposition of a suite of techniques based on the theory of polynomials, collectively referred to as polynomial methods, which have recently been applied to address several challenging problems in statistical…
Despite the recent successes of probabilistic programming languages (PPLs) in AI applications, PPLs offer only limited support for random variables whose distributions combine discrete and continuous elements. We develop the notion of…
In this paper, we present a unified analysis of methods for such a wide class of problems as variational inequalities, which includes minimization problems and saddle point problems. We develop our analysis on the modified Extra-Gradient…
Combinatorial optimization plays an important role in real-world problem solving. In the big data era, the dimensionality of a combinatorial optimization problem is usually very large, which poses a significant challenge to existing…
In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center…
We derive simple concentration inequalities for bounded random vectors, which generalize Hoeffding's inequalities for bounded scalar random variables. As applications, we apply the general results to multinomial and Dirichlet distributions…
The goal of this paper is to demonstrate the general modeling and practical simulation of random equations with mixture model parameter random variables. Random equations, understood as stationary (non-dynamical) equations with parameters…
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…
Makespan minimization in restricted assignment $(R|p_{ij}\in \{p_j, \infty\}|C_{\max})$ is a classical problem in the field of machine scheduling. In a landmark paper in 1990 [8], Lenstra, Shmoys, and Tardos gave a 2-approximation algorithm…
Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications…
We derive concentration inequalities for sums of independent and identically distributed random variables that yield non-asymptotic generalizations of several strong laws of large numbers including some of those due to Kolmogorov [1930],…
The thesis concentrates on two problems in discrete geometry, whose solutions are obtained by analytic, probabilistic and combinatoric tools. The first chapter deals with the strong polarization problem. This states that for any sequence…
Combinatorial optimization finds an optimal solution within a discrete set of variables and constraints. The field has seen tremendous progress both in research and industry. With the success of deep learning in the past decade, a recent…
This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav…
We derive novel concentration inequalities that bound the statistical error for a large class of stochastic optimization problems, focusing on the case of unbounded objective functions. Our derivations utilize the following key tools: 1) A…
In this work we show that with high probability the chromatic number of a graph sampled from the random regular graph model $\Gnd$ for $d=o(n^{1/5})$ is concentrated in two consecutive values, thus extending a previous result of Achlioptas…