Related papers: Concentration Inequalities for Random Sets
We consider an infectious disease spreading along the edges of a network which may have significant clustering. The individuals in the population have heterogeneous infectiousness and/or susceptibility. We define the out-transmissibility of…
In this note we derive a sharp concentration inequality for the supremum of a smooth random field over a finite dimensional set. It is shown that this supremum can be bounded with high probability by the value of the field at some…
How hard is it to achieve consensus in a social network under uncertainty? In this paper we model this problem as a social graph of agents where each vertex is initially colored red or blue. The goal of the agents is to achieve consensus,…
We consider the {\em clustering with diversity} problem: given a set of colored points in a metric space, partition them into clusters such that each cluster has at least $\ell$ points, all of which have distinct colors. We give a…
This paper develops upper bounds on the end-to-end transmission capacity of multi-hop wireless networks. Potential source-destination paths are dynamically selected from a pool of randomly located relays, from which a closed-form lower…
Given a large finite point set, $P\subset \mathbb R^2$, we obtain upper bounds on the number of triples of points that determine a given pair of dot products. That is, for any pair of positive real numbers, $(\alpha, \beta)$, we bound the…
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
We prove upper bounds on the rate, called "mixing rate", at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under non-local unitary evolution. For an ensemble consisting of two states,…
A pair of probability distributions over $\{0,1\}^n$ is said to be $(k,\delta)$-wise indistinguishable if all of the size $k$ marginals are within statistical distance at most $\delta$. Previous works introduced this concept and study when…
This article presents an algebraic topology perspective on the problem of finding a complete coverage probability of a one dimensional domain $X$ by a random covering, and develops techniques applicable to the problem beyond the one…
Reconstruction of population histories is a central problem in population genetics. Existing coalescent-based methods, like the seminal work of Li and Durbin (Nature, 2011), attempt to solve this problem using sequence data but have no…
For measuring the strength of visually-observed subpopulation differences, the Population Difference Criterion is proposed to assess the statistical significance of visually observed subpopulation differences. It addresses the following…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
Let $\zeta$ be Euclidean norm of the degree sequence of a graph normalized by the graph size. We prove that when the vertices of a graph are randomly colored with $s$ colors such that the fraction of vertices in each color class is bounded…
In this paper, we focus on susceptible-infected-susceptible dynamics on metapopulation networks, where nodes represent subpopulations, and where agents diffuse and interact. Recent studies suggest that heterogeneous network structure…
An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is generally NP-hard. We study the complexity of this problem in classes…
Given a correlation generated by a (possibly quantum) communication network, we study the amount of shared randomness required to generate it. We develop a novel upper bound for approximating distributions generated by arbitrary networks…
The set of answers to a query may be very large, potentially overwhelming users when presented with the entire set. In such cases, presenting only a small subset of the answers to the user may be preferable. A natural requirement for this…
Clustering problems are fundamental to unsupervised learning. There is an increased emphasis on fairness in machine learning and AI; one representative notion of fairness is that no single demographic group should be over-represented among…
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…